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An unconditional result about Grothendieck spaces

Author: Richard Haydon
Journal: Proc. Amer. Math. Soc. 100 (1987), 511-516
MSC: Primary 46B20
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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Article copyright: © Copyright 1987 American Mathematical Society

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