New criterion of the approximation property |
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Authors: | Ju Myung Kim |
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Affiliation: | National Institute for Mathematical Sciences 385-16, Doryong-dong, Yuseong-gu, Daejeon 305-340, Republic of Korea |
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Abstract: | This paper is concerned with the approximation property which is an important property in Banach space theory. We show that a Banach space X has the approximation property if (and only if), for every Banach space Y, the set of finite rank operators from X to Y is dense in the corresponding space of compact operators, in the usual topology of uniform convergence on compact sets. |
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Keywords: | Topology of compact convergence Approximation property |
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