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Proceedings of the American Mathematical Society

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

 

 

An unconditional result about Grothendieck spaces


Author: Richard Haydon
Journal: Proc. Amer. Math. Soc. 100 (1987), 511-516
MSC: Primary 46B20
DOI: https://doi.org/10.1090/S0002-9939-1987-0891155-7
MathSciNet review: 891155
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Abstract: It is shown that if $ X$ is a nonreflexive Banach spach such that every weak* convergent sequence in $ {X^ * }$ is also weakly convergent, then $ {X^ * }$ has a subspace isometric to $ {L_1}({\left\{ {0,1} \right\}^{{\omega _1}}})$


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DOI: https://doi.org/10.1090/S0002-9939-1987-0891155-7
Article copyright: © Copyright 1987 American Mathematical Society