Matrix maps and the isomorphic structure of BK spaces
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- by Jeff Connor PDF
- Proc. Amer. Math. Soc. 111 (1991), 45-50 Request permission
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 ${c_0}$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 45-50
- MSC: Primary 46B20; Secondary 46A45, 47B37
- DOI: https://doi.org/10.1090/S0002-9939-1991-1034884-8
- MathSciNet review: 1034884