Examples of asymptotically 1 Banach spaces
Spiros A. Argyros, Irene Deliyanni
Abstract
Two examples of asymptotic 1 Banach spaces are given. The first, Xu, 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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