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Autor Cobos, Fernando |
Documentos disponibles escritos por este autor (121)
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A procedure is given to reduce the interpolation spaces on an ordered pair generated by the function parameter t? (1 + |log t|)?b to the classical real interpolation spaces. Applications are given for Lorentz–Zygmund function spaces, Besov space[...]![]()
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We establish a formula for the measure of non-compactness of an operator interpolated by the general real method generated by a sequence lattice ?. The formula is given in terms of the norms of the shift operators in ?.![]()
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We investigate the limit J-spaces corresponding to the general real method. These interpolation spaces are defined by Banach sequence lattices and include those spaces that arise by the choice ? = 0 in the definition of the real method. We pay e[...]![]()
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With the help of limiting interpolation we determine the spaces obtained by iteration of approximation constructions. Then we apply the reiteration formula and limiting interpolation to investigate several problems on Besov spaces, including emb[...]![]()
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Besoy, Blanca F. ; Cobos, Fernando | 2019We determine the associate space of the logarithmic interpolation space (X0, X1)1,q,A where X0 and X1 are Banach function spaces over a ?-finite measure space (?, µ). Particularizing the results for the case of the couple (L1, L?) over a non-ato[...]![]()
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We determine the associate space of the logarithmic interpolation space (X0, X1)1,q,A where X0 and X1 are Banach function spaces over a ?-finite measure space (?, µ). Particularizing the results for the case of the couple (L1, L?) over a non-ato[...]![]()
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If T : A0 ! B boundedly and T : A1 ! B compactly, then a result of Lions{Peetre shows that T : A ! B compactly for a certain class of spaces A which are intermediate with respect to A0 and A1. We investigate to what extent such results can hold [...]![]()
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We work with Besov spaces Bp,q0,b defined by means of differences, with zero classical smoothness and logarithmic smoothness with exponent b. We characterize Bp,q0,b by means of Fourier-analytical decompositions, wavelets and semi-groups. We als[...]![]()
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Let ? be a bounded domain in Rn and denote by id? the restriction operator from the Besov space B1+n/p pq (Rn) into the generalized Lipschitz space Lip(1,??)(?). We study the sequence of entropy numbers of this operator and prove that, up to log[...]![]()
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We investigate compact operators between approximation spaces, paying special attention to the limit case. Applications are given to embeddings between Besov spaces.![]()
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Cobos, Fernando ; Fernández-Cabrera, Luz M. ; Martínez, Antón | Polish Acad Sciencies Inst Mathematics | 2005The paper establishes necessary and sufficient conditions for compactness of operators acting between general K -spaces, general J -spaces and operators acting from a J -space into a K -space. Applications to interpolation of compact operators a[...]![]()
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We establish a compactness interpolation result for bilinear operators of the type proved by Janson for bounded bilinear operators. We also give an application to compactness of convolution operators.![]()
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We characterize compact operators between complex interpolation spaces and between spaces obtained by using certain minimal methods in the sense of Aronszajn and Gagliardo. Applications to interpolation of compact operators are also given.![]()
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A theorem due to S. Janson, P. Nilsson, J. Peetre and M. Zafran [Proc. Lond. Math. Soc., III. Ser. 48, 283-299 (1984; Zbl 0532.46046)] states that for a Banach couple A such that _(A) is not closed in _(A) the real interpolation spaces A_,q and [...]![]()
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We work with logarithmic interpolation methods (A0,A1)?,q,A where ?=0 or 1. On the contrary to the case 0![]()
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Let S,q be the collection of all compact operators T on a (complex) Hilbert space H such that (INVALID INPUT),q(T) = (P1 n=1((n)sn(T))qn?1)1/q![]()
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Cobos, Fernando ; Fernández-Cabrera, Luz M. | 2020We review several results on duality of logarithmic interpolation spaces and applications to Besov spaces. We also establish some new results on Besov spaces with smoothness close to zero defined by differences.![]()
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We work with spaces (A0;A1)?;q;A which are logarithmic perturbations of the real interpolation spaces. We determine the dual of (A0;A1)?;q;A when0![]()
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We investigate dual spaces of interpolation spaces defined by means of polygons. We first show that dual spaces may fail to be intermediate spaces with respect to the dual N-tuple, and then we prove that dual spaces of J-spaces can be identified[...]![]()
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For a compact metric space X let ? be a finite Borel measure on X. The authors investigate the asymptotic behavior of eigenvalues of integral operators on L2(X, ?). These integral operators are assumed to have a positive definite kernel which sa[...]![]()
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We determine the asymptotic order of decay of eigenvalues of weakly singular integral operators. The singularities are of quite general form, containing power and logarithmic terms. We give a unified elementary proof of all known results in this[...]![]()
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This paper deals with Besov spaces of logarithmic smoothness B-p,T(0,b) formed by periodic functions. We study embeddings of B-p,T(0,b) into Lorentz-Zygmund spaces L-p,L-q(log L)(beta). Our techniques rely on the approximation structure of B-p,T[...]![]()
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The paper deals with ideals of operators for which the sequence of their entropy numbers(en(T)) belongs to a Lorentz-Marcinkiewicz space `,q, where is a so-called function parameter. In the case (t) = tp the classical Lorentz space `p,q results[...]![]()
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We establish two-sided estimates for entropy numbers of embeddings between certain weighted Banach sequence spaces with mixed norms. These estimates are‘‘almost’’ sharp, in the sense that upper and lower bounds differ only by logarithmic terms a[...]![]()
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We consider limiting real interpolation spaces defined by using powers of iterated logarithms and show their description by means of the J -functional. Our results allow to complement some estimates on approximation of stochastic integrals.![]()
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We study spectral properties of operators on logarithmic perturbations of the real interpolation spaces with ? = 0 or 1. We also establish estimates for the measure of non-compactness of operators interpolated by those methods.![]()
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We provide a simple algorithm that constructs an exact minimizer for the E-functional E(t, f ; L?, BV) = inf ?g?L??t ? f ? g?BV . Here L?, BV stand for the space of bounded functions and the space of functions with bounded variation on the inter[...]![]()
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We establish abstract extrapolation results for entropy numbers of operators in Banach spaces. The results apply to extrapolation in the source spaces and also in the target spaces. As an illustration of the abstract results, applications to lim[...]![]()
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We establish compactness results for extrapolation constructions which correspond to the well-known Lions-Peetre compactness theorems of interpolation theory. Applications are given to compactness of certain limiting Sobolev embeddings.![]()
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The paper establishes estimates for ideal measures of operators interpolated by the real method in terms of the measures of their restrictions to a sequence of spaces modelled on the intersection. It also shows that the estimates are optimal.![]()
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We characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space C-2. This answers a question posed by R. Grzaslewicz and K. John [7], who solved the corresponding problem for the real Hilbert space R-[...]![]()
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Cobos, Fernando ; Fernández-Cabrera, Luz M. | Institute of Mathematics. Polish Academy of Sciences | 2008We review several results on interpolation of Banach algebras and factorization of weakly compact homomorphisms. We also establish a new result on interpolation of multilinear operators.![]()
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The paper deals with the entropy ideals generated by the Lorentz- Marcinkiewicz spaces of the type ? ? (?) where ? is a function parameter. The entropy ideal generated by ? ? (?) is the set of all operators between Banach spaces whose sequence o[...]![]()
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Fernández-Cabrera, Luz M. ; Cobos, Fernando ; Hernández, Francisco L. ; Sánchez, Víctor M. | Cambridge University Press | 2004We study inclusion indices relative to an interpolation scale. Applications are given to several families of functions spaces.![]()
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Let (Y0, Y1) be a Banach couple and let Xj be a closed complemented subspace of Yj ; (j = 0; 1). We present several results for the general problem of finding necessary and sufficient conditions on the parameters (?, q) such that the real interp[...]![]()
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We study the interpolation properties of compact bilinear operators by the general real method among quasi- Banach couples. As an application we show that commutators of Calderón-Zygmund bilinear operators S : Lp × Lq -? Lr are compact provided [...]![]()
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We show that the classical Lions-Peetre compactness theorems for Banach spaces (which are the main tools for proving all known compactness results in interpolation theory) fail in the locally convex case. We also prove a positive result assuming[...]![]()
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We investigate how compact operators behave under J and K interpolation methods for N spaces and two parameters. First we study those methods: relationship with those already existing in the literature, estimates for the norms of interpolated op[...]![]()
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Cobos, Fernando ; Fernández-Martínez, Pedro ; Martínez, Antón | Polish Acad Sciencies Inst Mathematics | 1999We investigate the behaviour of the measure of Iron-compactness of an operator under real interpolation. Our results refer to general Banach couples. An application to the essential spectral radius of interpolated operators is also given.![]()
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Working in the setting of quasi-Banach couples, we establish a formula for the measure of non-compactness of bilinear operators interpolated by the general real method. The result applies to the real method and to the real method with a function[...]![]()
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We develop a method suitable for interpolation of uniformly absolutely continuous operators. We then apply this method to establishing compactness of operators and embeddings especially in the limiting situations, where the classical interpolati[...]![]()
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Given an operator ideal J , the author describes the behaviour under interpolation of deviations of a linear operator T from the closed surjective hull of J and the closed injective hull of J . General results obtained in a collaboration with A.[...]![]()
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We investigate limiting J-interpolation methods for general Banach couples, not necessarily ordered. We also show their relationship with the interpolation methods defined by the unit square.![]()
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We study limiting K- and J-methods for arbitrary Banach couples. They are related by duality and they extend the methods already known in the ordered case. We investigate the behaviour of compact operators and we also discuss the representation [...]![]()
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Working with interpolation methods associated to polygons, a result of Cobos and Peetre guarantees that the interpolated operator is compact provided all but two restrictions of the operator (located in adjacent vertices) are compact. We charact[...]![]()
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Besoy, Blanca F. ; Cobos, Fernando | 2019We derive interpolation formulae for the measure of non-compactness of operators interpolated by logarithmic methods with ? = 0, 1 between quasi-Banach spaces. Applications are given to operators between Lorentz-Zygmund spaces.![]()
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Besoy, Blanca F. ; Cobos, Fernando | 2020We derive interpolation formulae for the measure of non-compactness of operators interpolated by logarithmic methods with [?] = 0; 1 between quasi-Banach spaces. Applications are given to operators between Lorentz-Zygmund spaces.![]()
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This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value p[...]![]()
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Cobos, Fernando ; Fernández-Cabrera, Luz M. ; Manzano, Antonio ; Martínez, Antón | Heldermann Verlag | 2007Let A0 and A1 be quasi-Banach spaces with A0 ,! A1. By means of a direct approach, we show that the interpolation spaces on (A0;A1) generated by the function parameter tµ(1 + j log tj)¡b can be expressed in terms of classical real inter-polation[...]![]()
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We investigate pointwise domination property in operator spaces generated by Lorentz sequence spaces![]()
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We give a maximal description in the sense of Aronszajn-Gagliardo for the real method in the category of quasi-Banach spaces.![]()
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We establish an estimate for the measure of non-compactness of an interpolated operator acting from a J-space into a K-space. Our result refers to general Banach N-tuples. We also derive estimates for entropy numbers if some of the N-tuples redu[...]![]()
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We establish formulae for the measure of non-compactness of operators interpolated by limiting methods that come up by the choice ?=0 and ?=1 in the definition of the real method.![]()
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The authors consider multiparameter scales of interpolation spaces and prove a general form of the Wolff reiteration theorem [cf. T. H. Wolff, Lecture Notes Math. 908, 199- 204 (1982)] for n- tuples of Banach spaces. The proof, based on the use [...]![]()
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We give some new examples of bounded multilinear forms on th Hilbert spaces 2 and L2(0,?). We characterize those which are compact or Hilbert-Schmidt. In particular, we study m-linear forms (m ? 3) on 2 which can be regarded as the multilinear[...]![]()
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We study interpolation methods associated to polygons and establish estimates for the norms of interpolated operators. Our results explain the geometrical base of estimates in the literature. Applications to interpolation of weighted L(p)-spaces[...]![]()
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Let d ? N and let ? be a bounded Lipschitz domain in Rd. We prove that the embedding Id : Bd (?) ?? L (log L) (?) is nuclear if a![]()
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Cobos, Fernando ; Fernandez-Cabrera, Luz ; Kuehn, Thomas ; Ullrich, Tino | Academic Press-Elsevier Science | 2009We investigate the limit class of interpolation spaces that comes up by the choice ? = 0 in the definition of the real method. These spaces arise naturally interpolating by the J -method associated to the unit square. Their duals coincide with t[...]![]()
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Working on the d-torus, we show that Besov spaces Bps(Lp(logL)a) modelled on Zygmund spaces can be described in terms of classical Besov spaces. Several other properties of spaces Bps(Lp(logL)a) are also established. In particular, in the critic[...]![]()
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We compare Besov spaces B-p,q(0,b) with zero classical smoothness and logarithmic smoothness b defined by using the Fourier transform with the corresponding spaces:B-p,q(0,b) defined by means of the modulus of smoothness. In particular, we show [...]![]()
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Let ? = (A? , A?) , B? = (B? , B?) be Banach couples, let E be a Banach space and let T be a bilinear operator such that ||T(a, b)||? ? M[sub]j ||a||?[sub]j ||b||?[sub]j for a ? A? ? A?, b ? B? ? B?, j = 0, 1. If T : A°[sub]j × B°[sub]j ?? E com[...]![]()
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Let H denote a Hilbert space, T a compact operator on H, {sn(T)}1 n=1 the eigenvalues of |T|, and Sp (p > 0) the set of all such T for which {sn(T)}1 n=1 is in `p. If A and B are bounded linear operators on L2, say that B pointwise dominates A [...]![]()
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Cobos, Fernando ; Fernández-Martínez, Pedro ; Martínez, Antón ; Raynaud, Yves | Cambridge Univ Press | 1999We study the relationship between the dual of the #C-space defined by means of a polygon and the /-space generated by the dual N-tuple. The results complete the research started in [4]. Special attention is paid to the case when the N-tuple is f[...]![]()
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In a previous paper, the authors laid the foundations of a theory of Schatten±von Neumann classes 'p (0!p%¢) of trilinear forms in Hilbert space. This paper continues that research. In the n-dimensional case, it is shown that the best constant d[...]![]()
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We show a direct proof for the generalized Hardy’s inequality obtained by the first author Math. Nachr. 126, 281-300, 1986. Our techniques are elementary and work in the limit case which was not covered in [loc. cit.]. Some applications to eigen[...]![]()
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We determine the smallest Schatten class containing all integral operators with kernels in L(p)(L(p',q))symm, where 2![]()
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We study the interpolation properties of Asplund operators by the complex method, as well as by general J - and K-methods.![]()
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Cobos, Fernando ; Fernández-Cabrera, Luz M. ; Martínez, Antón | Gauthier-Villars/Editions Elsevier | 2006We show a necessary and sufficient condition on the lattice ? for the general real method (· , ·)? to preserve the Banach-algebra structure. As an application we derive factorization of weakly compact homomorphisms through interpolation properti[...]![]()
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The authors investigate the behaviour of bilinear operators under interpolation by the methods associated to polygons. These methods, working with N-tuples (N _ 3) of Banach spaces instead of couples, were introduced by F. Cobos and J. Peetre [P[...]![]()
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We prove that the classical Lions-Peetre compactness theorems for linear operators still hold for Lipschitz operators. As a consequence, we deduce that certain Uryson integral operators are compact. We also show that Lipschitz operators can be i[...]![]()
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The authors extend a result of K. Hayakawa [J. Math. Soc. Jap. 21, 189-199 (1969; Zbl 0181.137)], and prove: If T is a linear operator such that T: A0 ! B0, is bounded,and T: A1 ! B1 is compact, and moreover, A1 A0, then T: ¯ A,q ! ¯B,q is comp[...]![]()
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We describe the spaces obtained by applying the interpolation methods associated to polygons to N-tuples of weighted Lp-spaces, N-tuples of classical Lorentz spaces and some other N-tuples of function spaces.![]()
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We improve the known results on interpolation of strictly singular operators and strictly co-singular operators in several directions. Applications are given to embeddings between symmetric spaces.![]()
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We revised the known results on interpolation of the measure of noncompactness and we announce a new approach to establishing the interpolation formula for the real method.![]()
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We describe the behaviour under interpolation of a limit class of approximation spaces. We characterize them as extrapolation spaces. Moreover, we study the boundedness of certain operators on these spaces. As an application, we derive several r[...]![]()
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Cobos, Fernando ; Domínguez, Oscar ; Kühn, Thomas | 2018Let Bp,qs,?(?) be the Besov space with classical smoothness s and additional logarithmic smoothness of order ? on a bounded Lipschitz domain ? in Rd. For s1, s2 ? R, 1 ? p1, p2, q1, q2 ? ? and s1 ? s2 = d ? d(1/p2 ? 1/p1)+, we show a su?cient co[...]![]()
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We work with spaces of periodic functions on the d-dimensional torus. We show that estimates for L?-approximation of Sobolev functions remain valid when we replace L1 by the isotropic periodic Besov space B01;1 or the periodic Besovspace with do[...]![]()
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We show abstract versions for Banach couples of several limiting compact interpolation theorems established by Edmunds and Opic for couples of Lp spaces.![]()
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We show abstract versions for Banach couples of several limiting compact interpolation theorems established by Edmunds and Opic for couples of Lp spaces.![]()
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This article deals with K- and J-spaces defined by means of polygons. First we establish some reiteration formulae involving the real method, and then we study the behaviour of weakly compact operators. We also show optimality of the weak compac[...]![]()
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We establish interpolation formulae for operator spaces that are components of a given quasi-normed operator ideal.![]()
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The authors prove a representation theorem in terms of finite rank operators for operators´T on Banach spaces which satisfy sup n2N (log n) an(T)![]()
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Let E be a Banach function lattice such that L1[0; 1] ,! E ,! L1[0; 1]. We characterize the strict singularity of the embedding L1[0; 1] ,! E and the strict cosingularity of E ,! L1[0; 1] in terms of functionals de_ned by using characteristic fu[...]![]()
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We describe a new approach to interpolate by the complex method quasi-Banach couples formed by real-intermediate spaces. End-point cases are also considered, and applications are given to function spaces and to operator spaces.![]()
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We improve the known results on eigenvalue distributions of weakly singular integral operators having (power) order of the singularity equal to half of the dimension of the underlying domain. Moreover we show that our results are the best possible.![]()
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Compactness results of Cobos and Peetre [3] guarantee that the interpolated operator is compact assuming that all but two restrictions of the operator (located in adjacent vertices) are compact. Comparing these results with others in the literat[...]![]()
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On the Relationship between Interpolation of Banach Algebras and Interpolation of Bilinear Operators
We show that if the general real method (. , .)(Gamma) preserves the Banach-algebra Structure, then a bilinear interpolation theorem holds for (. , .)(Gamma).![]()
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Using limiting interpolation techniques we study the elationship between Besov spaces B0,?1/q p,q with zero classical smoothness and logarithmic smoothness ?1/q defined by means of differences with similar spaces 0,b,d p,q defined by means of th[...]![]()
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We show that if the duality between a Banach space A and its anti-dual A* is given by the inner product of a Hilbert space H, then (A, A*)1/2,2 = H = (A,A*)[l,2~, provided A satisfies certain mild conditions. We do not assume A is reflexive. App[...]![]()
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Interpolating compactness properties of operators is a long standing and important problem. In this paper, the authors consider the problem in a very general setting of Aronszajn-Gagliardo functors. In simplest terms they show that if T : A0 ! B[...]![]()
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Bashir, Zia ; Cobos, Fernando ; Karadzhov, Georgi E. | Matematisk Institut, Universitetsparken NY Munkegade | 2014We prove optimal embeddings of Calderon spaces built-up over function spaces defined in R-n with the Lebesgue measure into generalized Holder-Zygmund spaces in the super-critical and critical cases.![]()
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In this note we announce optimal embeddings of Calderon spaces built-up over function spaces defined in R-n with the Lebesgue measure into generalized Holder-Zygmund spaces in the super-critical case.![]()
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We describe the behavior of ideal variations under interpolation methods associated to polygons.![]()
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Bernhardsson, Bo ; Cobos, Fernando ; Kühn, Tomas ; Mondoc, Daniel ; Peetre, Jaak | Estonian Academy of Sciences | 2006So far trilinear forms have mostly been considered in low dimensions, in particular the dimension two (binary) case, and when the ring of scalars K is either the real numbers R or the complex ones C. The main aim in both situations has been to d[...]![]()
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We investigate the behaviour by general J- and K-methods of certain closed operator ideals. In particular, the results apply to weakly compact operators, Rosenthal operators and Banach–Saks operators.![]()
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We prove that if T: A0 ? B0 is compact and T: A1 ? B1 is compact (or T: A1 ? B1 is bounded and, then given any ? and q with 0![]()
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The behaviour of compactness under real interpolation is discussed. Classical results due to Krasnosel’skii, Lions-Peetre, Persson and Hayakawa are described, as well as others obtained very recently by Edmunds, Potter, Fernández and the author![]()
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Let (A(0)A(1)) and (B-0,B-1) be couples of quasi-Banach spaces and let T be a linear operator. We prove that if T:A(0) --> B-0 is compact and T: A(1) --> B-1 is bounded, then T: (A(0),A(1))(theta,q) --> (B-0,B-1)(theta,q) is also compact. Som[...]![]()
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We prove a reiteration theorem for interpolation methods defined by means of polygons, and a Wolff theorem for the case when the polygon has 3 or 4 vertices. In particular, we establish a Wolff theorem for Fernandez' spaces, which settles a prob[...]![]()
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We study spaces generated by applying the interpolation methods defined by a polygon ? to an N-tuple of real interpolation spaces with respect to a fixed Banach couple {X, Y }. We show that if the interior point (?,?) of the polygon does not lie[...]![]()
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Cobos, Fernando ; Fernández-Cabrera, Luz M. ; Martínez, Antón | Real Academia Ciencias Exactas Físicas Y Naturales | 2006This note deals with interpolation methods dened by means of polygons. We show necessary and sufcient conditions for compactness of operators acting from a J-space into a K-space.![]()
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We show that the behaviour under interpolation of 5x-class operators is not as good as it was supposed to be. An interpolation formula for Hilbert-Schmidt operators is also established.![]()
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We estimate the ideal measure of certain interpolated operators in terms of the measure of their restrictions to the intersection. The dual situation is also studied.: Special attention is paid to the ideal of weakly compact operators.![]()
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We establish representation theorems in terms of finite rank operators for some operator ideals defined by approximation numbers. We also study the stability under tensor product of these ideals.![]()
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The authors establish a number of results concerning normed ideals of multilinear forms in Banach spaces which extend the theory of trace ideals of operators on Hilbert space to such multilinear forms. For example, it is shown that the dual of t[...]![]()
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We show that, expcept in the trivial case p^ ^Qn ^2, the Lorentz operator space S ¿y is not isomorphic to a subspace of S for 1![]()
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Cobos, Fernando ; Fernández-Cabrera, Luz M. ; Martínez, Antón ; Pustylnik, Evgeniy | Cambridge University Press | 2002We show that certain interpolation results for compact operators established by Cobos and co-workers cannot be extended to general closed operator ideals. We shall also characterize compactness of an embedding in terms of functions related to th[...]![]()
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We continue the research on reiteration results between interpolation methods associated to polygons and the. real method. Applications are given to N-tuples of function spaces, or spaces or hounded linear operators and Banach algebras.![]()
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The authors study the limit case L1,q of the Lorentz- space approximation number ideals Lp,q. It is shown, using a suitable bilinear interpolation theorem that the ideals L1,q are tensor-stable. Moreover a telescoping sum representation theorem [...]![]()
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We review several results of Kühn, Peetre and the author on Schatten-von Neumann classes of multilinear forms. We recall also some of the open problems in this field![]()
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We study the description by means of the J-functional of logarithmic interpolation spaces (A0, A1) 1, q, A in the category of the p-normed quasi-Banach couples (0