Información del autor
Autor Villanueva, Ignacio |
Documentos disponibles escritos por este autor (48)
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We prove a characterization of the dual mixed volume in terms of functional properties of the polynomial associated with it. To do this, we use tools from the theory of multilinear operators on spaces of continuous functions. Along the way we re[...]texto impreso
Given a k-linear operator T from a product of C(K) spaces into a Banach space X, our main result proves the equivalence between T being completely continuous, T having an X-valued separately omega* - omega* continuous extension to the product of[...]texto impreso
We prove that the composition S(u(1),..., u(n)) of a multilinear multiple 2-summing operator S with 2-summing linear operators u(j) is nuclear, generalizing a linear result of Grothendieck.texto impreso
We prove that every countably additive polymeasure can be decomposed in a unique way as the sum of a "discrete" polymeasure plus a "continuous" polymeasure. This generalizes a previous result of Saeki.texto impreso
Let E be a complex Banach space and denote by H b (E) the space of all holomorphic functions f:E?C of bounded type, that is, bounded on bounded sets. It is known that f?H b (E) admits a factorization of the form f=g?S , with S a compact li[...]texto impreso
González Guillén, Carlos Eduardo ; Palazuelos Cabezón, Carlos ; Villanueva, Ignacio | Springer New York LLC | 2016In this work, we study a version of the general question of how well a Haar-distributed orthogonal matrix can be approximated by a random Gaussian matrix. Here, we consider a Gaussian random matrix (Formula presented.) of order n and apply to it[...]texto impreso
Villanueva, Ignacio ; Cabello Sánchez, Félix ; García, R. | Universidad de Extremadura, Departamento de Matemáticas | 2001This paper considers the problem of extending multilinear forms on a Banach space X to a larger space Y containing it as a closed subspace. For instance, if X is a subspace of Y and X0 ! Y 0 extends linear forms, then the induced Nicodemi operat[...]texto impreso
A new characterization of the Dunford-Pettis property in terms of the extensions of multilinear operators to the biduals is obtained. For the first time, multilinear characterizations of the reciprocal Dunford-Pettis property and Pelczynski's pr[...]texto impreso
Palazuelos Cabezón, Carlos ; Peralta Pereira, Antonio Miguel ; Villanueva, Ignacio | Polish Acad Sciencies Inst Mathematics | 2009In recent papers, the Right mid the Strong* topologies have been. introduced and studied on general Banach spaces We characterize different types of continuity for multilinear operators (joint, uniform, etc) with respect to the above topologies [...]texto impreso
Jarchow , Hans ; Palazuelos Cabezón, Carlos ; Pérez García, David ; Villanueva, Ignacio | Academic Press | 2007-12-15The aim of this paper is to investigate close relations between the validity of Hahn–Banach extension theorems for multilinear forms on Banach spaces and summability properties of sequences from these spaces. A case of particular importance occu[...]texto impreso
We consider the classes of “Grothendieck-integral” (G-integral)and “Pietsch-integral” (P-integral) linear and multilinear operators (see definitions below), and we prove that a multilinear operator between Banach spaces is G-integral (resp. P-in[...]texto impreso
We use polymeasures to characterize when a multilinear form defined on a product of C(K, X) spaces is integral.texto impreso
We study and characterize the integral multilinear operators on a product of C(K) spaces in terms of the representing polymeasure of the operator. Some applications are given. In particular, we characterize the Borel polymeasures that can be ext[...]texto impreso
Cooney, Tom ; Junge, Marius ; Navascués Cobo, Miguel ; Pérez García, David ; Villanueva, Ignacio | Springer | 2013Bipartite correlations generated by non-signalling physical systems that admit a finite-dimensional local quantum description cannot exceed the quantum limits, i.e., they can always be interpreted as distant measurements of a bipartite quantum s[...]texto impreso
Bombal Gordón, Fernando ; Fernández Unzueta, M. ; Villanueva, Ignacio | Sociedad Matemática Mexicana | 2004We use well known properties of the tensor product of l(p)-spaces to study the local structure of projective and injective tensor products of Banach spaces. In particular we give a simple proof of the fact that the injective (resp. projective) t[...]texto impreso
If K is an uncountable metrizable compact space, we prove a ‘factorization’ result for a wide variety of vector valued Borel measures ? defined on Kn. This result essentially says that for every such measure ? there exists a measure ?0 defined o[...]texto impreso
Villanueva, Ignacio ; Bombal Gordón, Fernando ; Pérez García, David | Oxford University Press | 2004We introduce a new class of multilinear p-summing operators, which we call multiple p-summing. Using them, we can prove several multilinear generalizations of Grothendieck’s “fundamental theorem of the metric theory of tensor products”. Several [...]texto impreso
Villanueva, Ignacio | Mathematical Institute of the Academy of Sciences of the Czech Republic | 2004Given Banach spaces X, Y and a compact Hausdor_ space K, we use polymeasures to give necessary conditions for a multilinear operator from C(K;X) into Y to be completely continuous (resp. unconditionally converging). We deduce necessary and suffi[...]texto impreso
Villanueva, Ignacio ; Bombal Gordón, Fernando | Faculty of Mathematics and Computer Science of Adam Mickiewicz University | 1998Let E1, . . . ,Ed be Banach spaces such that all linear operators from Ei into E_j (i 6= j) are weakly compact. The authors show that every continuous d-linear operator T on E1 × • • • × Ed to a Banach space F possesses a unique bounded multilin[...]texto impreso
In this paper, we improve some previous results about multiple p-summing multilinear operators by showing that every multilinear form from spaces is multiple p-summing for 1 p 2. The proof is based on the existence of a predual for the Banach s[...]texto impreso
In this paper, we characterize, for 1 ? ptexto impreso
Villanueva, Ignacio ; Cabello Sánchez, Félix ; García Herrera, Ricardo | Polish Academy of Sciences | 2000We show that a separable Banach space X has the Schur property if and only if every separately compact bilinear application from X into c0 is completely continuous, thus answering a question raised by Pe?czy?ski.texto impreso
In this paper we characterize those compact Hausdorff spaces such that (and ) have the Dunford-Pettis Property, answering thus in the negative a question posed by Castillo and González who asked if and have this property.texto impreso
Junge, M. ; Pérez García, David ; Palazuelos Cabezón, Carlos ; Villanueva, Ignacio ; Wolf, Michael | American Physical Society | 2009In this letter we show that the field of Operator Space Theory provides a general and powerful mathematical framework for arbitrary Bell inequalities, in particular regarding the scaling of their violation within quantum mechanics. We illustrate[...]texto impreso
Villanueva, Ignacio ; Palazuelos Cabezón, Carlos ; Peralta Pereira, Antonio Miguel | Oxford University Press | 2008-09We show that for every orthogonally additive scalar n-homogeneous polynomial P on a C*-algebra A there exists phi in A* satisfying P(x) = phi(x(n)), for each element x in A. The vector-valued analogue follows as a corollary.texto impreso
We show that, for every orthogonally additive homogeneous polynomial P on a space of continuous functions C(K) with values in a Banach space Y, there exists a linear operator S : C(K) -> Y such that P(f) = S(f(n)). This is the C(K) version of a[...]texto impreso
We show that, for bounded sequences in C(K,E), the polynomial sequential convergence is not equivalent to the pointwise polynomial sequential convergence. We introduce several conditions on E under which different versions of the result are true[...]texto impreso
Villanueva, Ignacio ; Peralta Pereira, Antonio Miguel ; Wright, J. D. Maitland ; Ylinen, Kari | Cambridge University Press | 2010-05We introduce the concept of quasi-completely continuous multilinear operators and use this concept to characterize, for a wide class of Banach spaces X1, …, Xk, the multilinear operators T : X1 × … × Xk ? X with an X-valued Aron–Berner extension.texto impreso
We characterize the positive radial continuous and rotation invariant valuations V defined on the star bodies of Rn as the applications on star bodies which admit an integral representation with respect to the Lebesgue measure. That is,V(K)=?Sn?[...]texto impreso
We show that a radial continuous valuation defined on the n-dimensional star bodies extends uniquely to a continuous valuation on the n-dimensional bounded star sets. Moreover, we provide an integral representation of every such valuation, in te[...]texto impreso
González-Guillén, Carlos E. ; Lancien, Cécilia ; Palazuelos Cabezón, Carlos ; Villanueva, Ignacio | Springer | 2017It is now a well-known fact that the correlations arising from local dichotomic measurements on an entangled quantum state may exhibit intrinsically non-classical features. In this paper we delve into a comprehensive study of random instances of[...]texto impreso
The purpose of this paper is to characterise the class of regular continuous multilinear operators on a product of C(K) spaces, with values in an arbitrary Banach space. This class has been considered recently by several authors in connection wi[...]texto impreso
We clarify and prove in a simpler way a result of Taskinen about symmetric operators on C(K-n), K an uncountable metrizable compact space. To do this we prove that, for any compact space K and any n is an element of N, the symmetric injective n-[...]texto impreso
We present a Riesz type representation theorem for multilinear operators defined on the product of C(K,X) spaces with values in a Banach space. In order to do this we make a brief exposition of the theory of operator valued polymeasures.[RESUMEN[...]texto impreso
González-Guillén, C.E. ; Jimenez, C.H. ; Palazuelos Cabezón, Carlos ; Villanueva, Ignacio | Springer | 2016It is well known that quantum correlations for bipartite dichotomic measurements are those of the form (Formula presented.), where the vectors ui and vj are in the unit ball of a real Hilbert space. In this work we study the probability of the n[...]texto impreso
Villanueva, Ignacio ; Bombal Gordón, Fernando ; Fernández Unzueta, M. | Polish Acad Sciencies Inst Mathematics | 2001The authors obtain in this paper a classification of projective tensor products of C(K) spaces, in terms of the behaviour of certain classes of multilinear operators on the product of the spaces, or the verification of certain Banach space prope[...]texto impreso
We present some results concerning the general theory of polymeasures. Among them, we point out an example of a polymeasure of bounded semivariation and unbounded variation, and two different characterizations of uniform polymeasures.texto impreso
What can we say about the spectra of a collection of microscopic variables when only their coarse-grained sums are experimentally accessible? In this paper, using the tools and methodology from the study of quantum nonlocality, we develop a math[...]texto impreso
A Banach space X has the Dunford–Pettis property (DPP) if and only if whenever (xn) and (pn) are weakly null sequences in X and X*, respectively, we have pn(xn)? 0. Freedman introduced a stricly weaker version of the DPP called the alternative D[...]texto impreso
Peralta Pereira, Antonio Miguel ; Villanueva, Ignacio ; Wright, J. D. Maitland ; Ylinen, Kari | Elsevier | 2007-01-15Let X be a Banach space. Then there is a locally convex topology for X, the “Right topology,” such that a linear map T, from X into a Banach space Y, is weakly compact, precisely when T is a continuous map from X, equipped with the “Right” topol[...]texto impreso
Villanueva, Ignacio ; Junge, Marius ; Pérez García, David ; Wolf, Michael ; Palazuelos Cabezón, Carlos | Springer | 2008We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount [...]texto impreso
Villanueva, Ignacio ; Junge, Marius ; Pérez García, David ; Wolf, Michael ; Palazuelos Cabezón, Carlos | Springer | 2010-12In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order ?(?n?Log2n) when observables with n possible outcomes are used. A central tool in the analysis is a close[...]texto impreso
Junge, M. ; Pérez García, David ; Palazuelos Cabezón, Carlos ; Villanueva, Ignacio ; Wolf, Michael | Springer | 2010In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order $\sqrt{n}$ (up to a logarithmic factor) when observables with n possible outcomes are used. A central tool[...]texto impreso
Villanueva, Ignacio ; Pérez García, David | Matematisk Institut, Universitetsparken NY Munkegade | 2005We prove that a tensor norm alpha (defined on tensor products of Hilbert spaces) is the Hilbert-Schmidt norm if and only if l(2) circle times(...)circle times l(2), endowed with the norm alpha, has an unconditional basis. This extends a classica[...]texto impreso
We introduce a notion of unconditionally converging multilinear operator which allows to extend many of the results of the linear case to the multilinear case. We prove several characterizations of these multilinear operators (one of which seems[...]texto impreso
Villanueva, Ignacio ; Pérez García, David ; Cabello Sánchez, Félix | Oxford University Press | 2006-10We describe complemented Copies Of l(2) both in C(K-1)circle times C-pi(K-2) when at least one of the compact spaces K-i is not scattered and in L-1(mu(1))circle times L-is an element of(1)(mu(2)) when at least one of the measures is not atomic.[...]texto impreso
Villanueva, Ignacio ; Peralta Pereira, Antonio Miguel ; Wright, J. D. Maitland ; Ylinen, Kari | Cambridge University Press | 2010The strong* topology s_(X) of a Banach space X is defined as the locally convex topology generated by the seminorms x 7! kSxk for bounded linear maps S from X into Hilbert spaces. The w-right topology for X, _(X), is a stronger locally convex to[...]texto impreso
Using a ‘reasonable’ measure in , the space of 2-homogeneous polynomials on ?1n, we show the existence of a set of positive (and independent of n) measure of polynomials which do not attain their norm at the vertices of the unit ball of ?1n. Ne[...]