Papers
New criterion of the approximation property
- AuthorJu Myung Kim
- JournalJournal of Mathematical Analysis and Applications 345 (2008
- Link https://doi.org/10.1016/j.jmaa.2008.05.002
- Classification of papersSCI
- KeywordTopology of compact convergence; Approximation property
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.
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.