Matrix maps and the isomorphic structure of BK spaces

Author:
Jeff Connor

Journal:
Proc. Amer. Math. Soc. **111** (1991), 45-50

MSC:
Primary 46B20; Secondary 46A45, 47B37

MathSciNet review:
1034884

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Abstract: This note gives a characterization of BK spaces that contain isomorphic copies of in terms of matrix maps and a sufficient condition for a matrix map from into a BK space to be a compact operator. The primary tool used in this note is the Bessaga-Pelczynski characterization of Banach spaces which contain isomorphic copies of . It is shown that weakly compact matrix maps on are compact and that, if is a BK space such that there is a matrix such that and is not strongly conull, then must contain an isomorphic copy of .

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1991-1034884-8

Keywords:
BK space,
conull,
compact operator,
unconditionally convergent

Article copyright:
© Copyright 1991
American Mathematical Society