Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/78332
Type: Artigo de periódico
Title: The approximation property for spaces of holomorphic functions on infinite dimensional spaces II
Author: Dineen, S
Mujica, J
Abstract: Let H(U) denote the vector space of all complex-valued holomorphic functions on an open subset U of a Banach space E. Let tau(omega) ancl tau(delta) respectively denote the compact-ported topology and the bornological topology on H(U). We show that if E is a Banach space with a shrinking Schauder basis, and with the property that every continuous polynomial on E is weakly continuous on bounded sets, then (H(U), tau(omega)) and (H(U), tau(delta)) have the approximation property for every open subset U of E. The classical space c(0), the original Tsirelson space T* and the Tsirelson*-James space T(J)* are examples of Banach spaces which satisfy the hypotheses of our main result. Our results arc actually valid for Riemann domains. (C) 2010 Elsevier Inc. All rights reserved.
Subject: Holomorphic function
Banach space
Schauder basis
Pseudoconvex Riemann domain
Country: EUA
Editor: Academic Press Inc Elsevier Science
Rights: fechado
Identifier DOI: 10.1016/j.jfa.2010.04.001
Date Issue: 2010
Appears in Collections:Artigos e Materiais de Revistas Científicas - Unicamp

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