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|Type:||Artigo de periódico|
|Title:||The approximation property for spaces of holomorphic functions on infinite dimensional spaces III|
|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 .|
|Appears in Collections:||Artigos e Materiais de Revistas Científicas - Unicamp|
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