Departamento de Matemáticas, Universidad Pública de Navarra, Pamplona 31006, Spain
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.
We show that the -convexified Tsirelson space for 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.