The approximation property for spaces of holomorphic functions on infinite dimensional spaces II |
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Authors: | Seán Dineen |
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Institution: | a Department of Mathematics, University College Dublin, Belfield, Dublin 4, Ireland b Departamento de Matemática, Universidade Estadual de Campinas, Rua Sergio Buarque de Holanda 651, 13083-859 Campinas, SP, Brazil |
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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 τω and τδ 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),τω) and (H(U),τδ) have the approximation property for every open subset U of E. The classical space c0, the original Tsirelson space T∗ and the Tsirelson∗-James space are examples of Banach spaces which satisfy the hypotheses of our main result. Our results are actually valid for Riemann domains. |
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Keywords: | Holomorphic function Banach space Schauder basis Pseudoconvex Riemann domain |
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