Examples of asymptotically \ell_^1 Banach spaces

Abstract

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.

References in corpus (2)

• Banach Spaces Of The Type Of Tsirelson
• A remark about distortion