Compact holomorphic mappings on Banach spaces and the approximation property |
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| Authors: | Richard M Aron M Schottenloher |
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| Institution: | 1. Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506, USA;2. School of Mathematics, Trinity College, Dublin, Ireland;3. Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506 USA;4. Mathematisches Institut der Universität, 8 München 2, Germany |
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| Abstract: | Let (E) be the space of complex valued holomorphic functions on a complex Banach space E. The approximation property for (E), endowed with various natural locally convex topologies, is studied. For example, (E) with the compact-open topology has the approximation property if and only if E has the approximation property. In order to characterize when (E) has the approximation property for topologies other than the compact-open, the notion of a compact holomorphic map between Banach spaces in introduced and studied. |
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