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

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

F. Albiac and C. Leránoz

Departamento de Matemáticas, Universidad Pública de Navarra, Pamplona 31006, Spain

Received 16 July 2009; Accepted 3 December 2009

Academic Editor: Simeon Reich

Copyright © 2009 F. Albiac and C. Leránoz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.