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If E and F are complex Banach spaces, and fixing a balanced open subset U of E, we let Hb=(Hb(U;F),?b) denote the space of all mappings f:U?F which are holomorphic of bounded type, endowed with its natural topology ?b; clearly, Hb is a Fréchet s[...]texto impreso
Let f be a holomorphic function on a complex normed space E. The possibility of extending f to the completion of E has been studied by Hirschowitz, Noverraz, Dineen, and Dineen-Noverraz. Here, following the ideas in [4, section 6.1], we study th[...]texto impreso
Let f be a holomorphic function on a complex normed space E. The possibility of extending f to the completion of E has been studied by Hirschowitz, Noverraz, Dineen, and Dineen-Noverraz. Here, following the ideas in [4, section 6.1], we study th[...]texto impreso
Ansemil, José María M. ; Blasco Contreras, Fernando ; Ponte, Socorro | Suomalainen tiedeakatemia | 2000In this paper we point out some relations concerning properties (BB)(n) and (BB)(n,s) related to the "Probleme des topologies" of Grothendieck and give a first example of a Frechet space with the (BB)(2) property but without the (BB)(3) property.texto impreso
In this paper we prove that given any two disjoint balls in an infinite dimensional complex Banach space, there exists an entire function which is bounded on one and unbounded on the other.texto impreso
Let U be an open subset of a complex locally convex space E, let F be a closed subspace of E, and let PI:E --> E/F be the canonical quotient mapping. In this paper we study the induced mapping PI*, taking f is-an-element-of H(b)(PI(U))--> f ci[...]texto impreso
Ansemil, José María M. ; López-Salazar Codes, Jerónimo ; Ponte, Socorro | Polish Acad Sciencies Inst Mathematics | 2011Let X be an infinite-dimensional complex Banach space. Very recently, several results on the existence of entire functions on X bounded on a given ball B(1) subset of X and unbounded on another given ball B(2) subset of X have been obtained. In [...]texto impreso
In this work we investigate the inverse approximation problems in the Lebesgue and Smirnov spaces with weights satisfying the so-called Muckenhoupt's Ap condition in terms of the -th mean modulus of smoothness, > 0. We obtain a converse theore[...]texto impreso
In this paper we prove, among other things, that the space of all holomorphic functions on an open subset U of a complex metrizable space E, endowed with the Nachbin ported topology, is metrizable only if E has finite dimension. This answers a q[...]texto impreso
In this paper we prove several results on the existence of analytic functions on an infinite dimensional real Banach space which are bounded on some given collection of open sets and unbounded on others. In addition, we also obtain results on th[...]texto impreso
Ansemil, José María M. ; Blasco Contreras, Fernando ; Ponte, Socorro | Università del Salento | 1997A property P of locally convex spaces is called a three-space property whenever the following implication holds: if both a closed subspace F and the corresponding quotient E/F of a locally convex space E have P then E has P as well. The authors [...]texto impreso
Properties (BB)n, n = 2, 3, ... on a locally convex space (see the definition below) have been recently introduced ([10]). They are interesting, among other things, in connection with the study of natural topologies on spaces of polynomials, mul[...]texto impreso
An example of a Frechet space E is given such that the space of n-homogeneous continuous polynomials on E, endowed with any of the natural topologies usually considered on it, is quasinormable for every n is an element of N. This space has the p[...]texto impreso
Ansemil, José María M. ; Aron, Richard M. ; Ponte, Socorro | European Mathematical Society | 2009-06We prove the impossibility of expressing the space of entire functions on any infinite dimensional complex Banach space with a Schauder basis E as a countable union of spaces of entire functions that are bounded on countable open covers of E.texto impreso
Ansemil, José María M. ; Ponte, Socorro | Real Academia de Ciencias Exactas, Físicas y Naturales | 2000This informative paper surveys applications of results in the theory of topological tensor products of Fréchet or (DF)-spaces to the topological structure of spaces of n-homogeneous continuous polynomials. Recent progress about tensor products w[...]
