Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/78333
Type: Artigo de periódico
Title: The approximation property for spaces of holomorphic functions on infinite dimensional spaces III
Author: Dineen, S
Mujica, J
Abstract: Let denote the vector space of all complex-valued holomorphic functions on an open subset U of a Banach space E, with the Nachbin compact-ported topology. Let denote the vector space of all complex-valued holomorphic germs on a compact subset K of E, with its natural inductive limit topology. Let denote the Banach space of all continuous complex-valued m-homogeneous polynomials on E. When E has a Schauder basis, we show that has the approximation property for every compact subset K of E if and only if has the approximation property for every . When E has an unconditional Schauder basis, we show that has the approximation property for every pseudoconvex open subset U of E if and only if has the approximation property for every . These theorems apply in particular to the classical Banach spaces and , and to the original Tsirelson space .
Subject: Holomorphic function
Holomorphic germ
Homogeneous polynomial
Banach space
Schauder basis
Approximation property
Country: EUA
Editor: Springer
Rights: aberto
Identifier DOI: 10.1007/s13398-012-0065-7
Date Issue: 2012
Appears in Collections:Artigos e Materiais de Revistas Científicas - Unicamp

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