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,[...]texto impreso
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[...]texto impreso
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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.texto impreso
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[...]texto impreso
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[...]texto impreso
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.texto impreso
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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))[...]texto impreso
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[...]texto impreso
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;[...]texto impreso
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; [...]texto impreso
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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[...]texto impreso
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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[...]texto impreso
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[...]texto impreso
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 ktexto impreso
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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[...]texto impreso
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[...]texto impreso
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))[...]texto impreso
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Garrido, M. Isabel ; Jaramillo Aguado, Jesús Ángel ; Llavona, José G. | Elsevier Science | 2005-06-05On every real Banach space X we introduce a locally convex topology tau(p), canonically associated to the weak-polynomial topology w(P). It is proved that tau(p) is the finest locally convex topology on X which is coarser than w(P). Furthermore,[...]texto impreso
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. Every compact (linear) operator is polynomially continuous. We prove that every[...]texto impreso
Gutiérrez, Joaquín M. ; Jaramillo Aguado, Jesús Ángel ; Llavona, José G. | Universidad de Extremadura, Departamento de Matemáticas | 1995In this paper we survey a large part of the results on polynomials on Banach spaces that have been obtained in recent years. We mainly look at how the polynomials behave in connection with certain geometric properties of the spaces.texto impreso
The aim of this article is to prove a representation theorem for orthogonally additive polynomials in the spirit of the recent theorem on representation of orthogonally additive polynomials on Banach lattices but for the setting of Riesz spaces.[...]texto impreso
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Bombal Gordón, Fernando ; Llavona, José G. | Real Academia de Ciencias Exactas, Físicas y Naturales | 1976Let E and X be real Banach and locally convex spaces, respectively. Let Ccn(E,X) denote the space of n times continuously Hadamard differentiable functions f:E?X, endowed with the locally convex topology generated by the seminorms of the form f?[...]texto impreso
Let E = F' where F is a complex Banach space and let pi(1) : E" - E circle plus F-perpendicular to --> E be the canonical projection. Let P(E-n) be the space of the complex valued continuous n-homogeneous polynomials defined in E. We characteri[...]texto impreso
García González, Ricardo ; Jaramillo Aguado, Jesús Ángel ; Llavona, José G. | Wiley-Blackwell | 2011In this paper we show that the Aron-Berner type extension of polynomials preserves the P-continuity property. To this end we introduce a new version of Goldstine's Theorem for locally complemented subspaces.texto impreso
This paper is concerned with the study of the set P-1 (0), when P varies over all orthogonally additive polynomials on l(p) and L (p) spaces. We apply our results to obtain characterizations of the weak-polynomial topologies associated to this c[...]texto impreso
This is a survey paper concerning:\par 1) relations between spaces of weakly continuous functions on Banach spaces and their weak topologies;\par 2) weakly continuous and weakly differentiable function spaces in relation with the extension of [...]texto impreso
This paper is an expository presentation of a large part of the results, about zeros of real polynomials on Banach spaces, that have been obtained in recent years. Also new results, for orthogonally additive polynomials on L-p spaces, are given