Abstract and Applied Analysis
Volume 2009 (2009), Article ID 780287, 6 pages
doi:10.1155/2009/780287

The Tsirelson Space 𝒯(p) Has a Unique Unconditional Basis up to Permutation for 0<p<1

Abstract

We show that the p-convexified Tsirelson space 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.