The Tsirelson space \(\mathcal T(p)\) has a unique unconditional basis up to permutation for \(0<p<1\). (English) Zbl 1192.46002

Albiac, F.; Leránoz, C.

Abstr. Appl. Anal. 2009, Article ID 780287, 6 p. (2009).

Summary: We show that the \(p\)-convexified Tsirelson space \(\mathcal T{(p)}\) for \(0<p<1\) and all its complemented subspaces with unconditional basis have unique unconditional basis up to permutation. The techniques involved in the proof are different from the methods that have been used in all the other uniqueness results in the nonlocally convex setting.

MSC:

46A16

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)

Keywords:

\(p\)-convexified Tsirelson; unique unconditional basis up to permutation

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