On sequences without weak* convergent convex block subsequences

Haydon, Richard; Levy, Mireille; Odell, Edward

doi:10.1090/S0002-9939-1987-0883407-1

On sequences without weak$^ \ast$ convergent convex block subsequences
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Proc. Amer. Math. Soc. 100 (1987), 94-98 Request permission

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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