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A Note on Banach Spaces Containing ℓ1

Published online by Cambridge University Press:  20 November 2018

Robert H. Lohman
Robert H. Lohman*
Affiliation:
Department of Mathematics, Kent State UniversityKent, OH 44242, U.S.A.
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Abstract

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If Y is a subspace of a Banach space X, either Y contains an isomorphic copy of ℓ1 or each weak Cauchy sequence in X/Y has a subsequence that is the image under the quotient mapping of a weak Cauchy sequence in X. If X is weakly sequentially complete and Y is reflexive, X/Y is weakly sequentially complete. Related structural results are given.

Keywords

46B1546A35Banach spaceweakly sequentially completeSchur property
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 3 , 01 September 1976 , pp. 365 - 367
Copyright
Copyright © Canadian Mathematical Society 1976

References

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