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Proceedings of the American Mathematical Society

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

 

 

Banach spaces which always contain supremum-attaining elements


Author: Peter D. Morris
Journal: Proc. Amer. Math. Soc. 83 (1981), 496-498
MSC: Primary 46B20
DOI: https://doi.org/10.1090/S0002-9939-1981-0627677-8
MathSciNet review: 627677
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Abstract: It is proved that if a weakly compactly generated Banach space $ X$ has the property that, for every closed, bounded convex subset $ K$ of $ {X^ * }$, there exists a nonzero element of $ X$ which attains its supremum on $ K$, then $ X$ contains no copy of $ {l^1}$.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0627677-8
Article copyright: © Copyright 1981 American Mathematical Society