The approximation property for spaces of holomorphic functions on infinite dimensional spaces II

Autor(es)

Dineen, Sean ^[1] ; Mujica, Jorge ^[2]

Afiliação do(s) autor(es)

^[1] Univ Coll Dublin, Dept Math, Dublin 4 - Ireland

^[2] Univ Estadual Campinas, Dept Matemat, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF FUNCTIONAL ANALYSIS; v. 259, n. 2, p. 545-560, JUL 15 2010.
• Citações Web of Science: 8

Resumo

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. (AU)

• Processo FAPESP: 06/02378-7 - Análise em dimensão infinita
• Beneficiário: Jorge Tulio Mujica Ascui
• Modalidade de apoio: Auxílio à Pesquisa - Temático