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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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 $ {c_0}$ in terms of matrix maps and a sufficient condition for a matrix map from $ {l_\infty }$ 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 $ {c_0}$. It is shown that weakly compact matrix maps on $ {l_\infty }$ are compact and that, if $ E$ is a BK space such that there is a matrix $ A$ such that $ {c_0} \subseteq {E_A}$ and $ {E_A}$ is not strongly conull, then $ E$ must contain an isomorphic copy of $ {c_0}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1034884-8
PII: S 0002-9939(1991)1034884-8
Keywords: BK space, conull, compact operator, unconditionally convergent
Article copyright: © Copyright 1991 American Mathematical Society