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Proceedings of the American Mathematical Society

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On sequences without weak$ \sp \ast$ convergent convex block subsequences


Authors: Richard Haydon, Mireille Levy and Edward Odell
Journal: Proc. Amer. Math. Soc. 100 (1987), 94-98
MSC: Primary 46B15; Secondary 03E50
MathSciNet review: 883407
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Abstract: Let $ X$ be a Banach space such that $ {X^ * }$ contains a bounded sequence without a weak* convergent convex block subsequence. Then, subject to Martin's Axiom and the negation of the Continuum Hypothesis, $ X$ contains $ {l_1}(\mathfrak{c})$. With the same assumption, every nonreflexive Grothendieck space has $ {l_\infty }$ as a quotient.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0883407-1
Article copyright: © Copyright 1987 American Mathematical Society