A Banach space with a symmetric basis which contains no $\ell _ p$ or $c_0$, and all its symmetric basic sequences are equivalent

We give an intrinsic characterisation of the separable reflexive Banach spaces that embed into separable reflexive spaces with an unconditional basis all of whose normalised block sequences with the same growth rate are equivalent. This uses methods of E. Odell and T. Schlumprecht.

The Tsirelson space $𝒯 (p)$ has a unique unconditional basis up to permutation for $0 < p < 1$ .

Albiac, F., Leránoz, C. (2009)

Abstract and Applied Analysis

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On a result of Olevskiĭ : a uniformly bounded orthonormal sequence is not a basis for $C [0, 1]$

A. Pełczynski (1973-1974)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

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