2016
DOI: 10.48550/arxiv.1612.08127
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Absolutely convex sets of large Szlenk index

Philip A. H. Brooker

Abstract: Let X be a Banach space and K an absolutely convex, weak * -compact subset of X. We study consequences of K having a large or undefined Szlenk index, and subsequently derive a number of related results concerning basic sequences and universal operators. We show that if X has a countable Szlenk index then X admits a subspace with a basis and with Szlenk indices comparable to the Szlenk indices of X. If X is separable, then X also admits a quotient with these same properties. We also show that for a given ordina… Show more

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