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

Author(s)

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

Affiliation

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

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

• Document type: Journal article
• Source: JOURNAL OF FUNCTIONAL ANALYSIS; v. 259, n. 2, p. 545-560, JUL 15 2010.
• Web of Science Citations: 8

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. (AU)

• FAPESP's process: 06/02378-7 - Infinite Dimensional Analysis
• Grantee: Jorge Tulio Mujica Ascui
• Support Opportunities: Research Projects - Thematic Grants