Información del autor
Autor Llavona, José G. |
Documentos disponibles escritos por este autor (38)
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This paper is a survey of approximation results and methods by smooth functions in Banach spaces. The topics considered in the paper are the following: approximation by polynomials by C-k-functions using the method of smooth partitions of unity,[...]![]()
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This self-contained book brings together the important results of a rapidly growing area.As a starting point it presents the classic results of the theory. The book covers such results as: the extension of Wells' theorem and Aron's theorem for t[...]![]()
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In this note we study the relationship between compactness and weak compactness of a continuous homomorphism A from Cco(S) into Cco(T) and the associated continuous function ' : T ! S, where S and T are completely regular Hausdorff spaces.![]()
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Let E and F be Banach spaces and let Cwu(E) be the Fréchet algebra of real-valued functions on E which are uniformly weakly continuous when restricted to any bounded subset of E. Homomorphisms, and properties of such homomorphisms, between Cwu(E[...]![]()
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Let E, F be real Banach spaces, U subset-or-equal-to E and V subset-equal-to F non-void open subsets and C(k)(U) the algebra of real-valued k-times continuously Frechet differentiable functions on U, endowed with the compact open topology of ord[...]![]()
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A characterization of uniform continuity for maps between unit balls of real Banach spaces is given in terms of universal properties. Also, it is shown that the classes of compact and weakly compact composition operators induced by such maps agree.![]()
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Consider the following possible properties which a Banach space X may have: (P): If (x(j)) and (y(j)) are are bounded sequences in X such that for all n greater than or equal to 1 and for every continuous n-homogeneous polynomial P on X, P(x(j))[...]![]()
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The main result in this paper is a representation theorem for homogeneous orthogonally additive polynomials on Banach lattices. The representation theorem is used to study the linear span of the set of zeros of homogeneous real-valued orthogonal[...]![]()
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We begin this paper with a general study of algebra homomorphisms between algebras of continuous real functions on completely regular topological spaces; we study their automatic continuity and we characterize them as induced by continuous maps;[...]![]()
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Let E and F be two real Banach spaces. For n = 0, 1, ...,1, let Cnw ub(E; F) be the space of n-times continuously differentiable functions f: E ! F such that, for each integer j _ n and each x 2 E, both the jth derivative mapping fj : E ! P(jE; [...]![]()
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Let E and F be two Banach spaces and let A be a nonempty subset of E . A mapping f:A?F is said to be weakly continuous if it is continuous when A has the relative weak topology and F has the topology of its norm. Let A={E} , B= {A?E:A is[...]![]()
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Given a multi-index sequence necessary and sufficient conditions are given for the existence of a regular Borel polymeasure on the unit interval such that . This problem will be called the weak multilinear Hausdorff problemof moments for . Compa[...]![]()
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Llavona, José G. ; Linares Briones, Pablo ; Ibort Latre, Luis Alberto | American Mathematical Society | 2010A multilinear generalization of the trigonometric problem of moments is presented and discussed. The moments c(k), k is an element of Z(n) of a regular Borel polymeasure gamma on T(n) are characterized by means of a norm parallel to . parallel t[...]![]()
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Llavona, José G. ; Linares Briones, Pablo ; Ibort Latre, Luis Alberto | European Mathematical Society | 2009-06We present a new proof of a Sundaresan's result which shows that the space of orthogonally additive polynomials P-0((k)l(p)) is isometrically isomorphic to l(p/p-k) if k![]()
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Given a Banach space X and an integer n, the existence of an n-homogeneous polynomial which is not uniformly continuous with respect to the polynomial topology on B-X is investigated. We provide a complete characterization for some classical Ban[...]![]()
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A characterization of dense polynomial algebras is obtained for a certain class of p-continously differentiable Fréchet functions between real Banach spaces. In order to study this result a new approximation property in Banach spaces, the bounde[...]![]()
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A mapping between Banach spaces is said to be polynomially continuous if its restriction to any bounded set is uniformly continuous for the weak polynomial topology. A Banach space X has property(RP) if given two bounded sequences (u(j)), (v(j))[...]