The Tsirelson Space &#x1D4AF;(p) Has a Unique Unconditional Basis up to Permutation for 0<p<1

We show that the p-convexified Tsirelson space &#x1D4AF;(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 uniq...

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Main Authors: F. Albiac, C. Leránoz
Format: Article
Language:English
Published: Wiley 2009-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2009/780287
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author F. Albiac
C. Leránoz
author_facet F. Albiac
C. Leránoz
author_sort F. Albiac
collection DOAJ
description We show that the p-convexified Tsirelson space &#x1D4AF;(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.
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series Abstract and Applied Analysis
spelling doaj-art-afa9760e47b94f07be54ef0a090a868d2025-08-20T02:19:07ZengWileyAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/780287780287The Tsirelson Space &#x1D4AF;(p) Has a Unique Unconditional Basis up to Permutation for 0<p<1F. Albiac0C. Leránoz1Departamento de Matemáticas, Universidad Pública de Navarra, Pamplona 31006, SpainDepartamento de Matemáticas, Universidad Pública de Navarra, Pamplona 31006, SpainWe show that the p-convexified Tsirelson space &#x1D4AF;(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.http://dx.doi.org/10.1155/2009/780287
spellingShingle F. Albiac
C. Leránoz
The Tsirelson Space &#x1D4AF;(p) Has a Unique Unconditional Basis up to Permutation for 0<p<1
Abstract and Applied Analysis
title The Tsirelson Space &#x1D4AF;(p) Has a Unique Unconditional Basis up to Permutation for 0<p<1
title_full The Tsirelson Space &#x1D4AF;(p) Has a Unique Unconditional Basis up to Permutation for 0<p<1
title_fullStr The Tsirelson Space &#x1D4AF;(p) Has a Unique Unconditional Basis up to Permutation for 0<p<1
title_full_unstemmed The Tsirelson Space &#x1D4AF;(p) Has a Unique Unconditional Basis up to Permutation for 0<p<1
title_short The Tsirelson Space &#x1D4AF;(p) Has a Unique Unconditional Basis up to Permutation for 0<p<1
title_sort tsirelson space x1d4af p has a unique unconditional basis up to permutation for 0 p 1
url http://dx.doi.org/10.1155/2009/780287
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