Examples of asymptotically \ell_^1 Banach spaces

Mathematics – Functional Analysis

Scientific paper

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Scientific paper

Two examples of asymptotic $\ell_{1}$ Banach spaces are given. The first,
$X_{u}$, has an unconditional basis and is arbitrarily distortable. The
second, $X$, does not contain any unconditional basic sequence. Both are
spaces of the type of Tsirelson. We thus answer a question raised by
W.T.Gowers.

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