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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On sequences spanning a complex $ l_1$ space


Author: Leonard E. Dor
Journal: Proc. Amer. Math. Soc. 47 (1975), 515-516
MSC: Primary 46B15
DOI: https://doi.org/10.1090/S0002-9939-1975-0358308-X
MathSciNet review: 0358308
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Abstract: If $ ({f_n})$ is a bounded sequence in a complex Banach space $ B$, and no subsequence of $ ({f_n})$ is weakly Cauchy, then a subsequence of $ ({f_n})$ is equivalent to the unit vector basis of the complex $ {l_1}$ space.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0358308-X
Keywords: Sequential compactness, pointwise convergence
Article copyright: © Copyright 1975 American Mathematical Society