The Tsirelson Space 𝒯(p) Has a Unique Unconditional Basis up to Permutation for 0<p<1
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 uniq...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| 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 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. |
| format | Article |
| id | doaj-art-afa9760e47b94f07be54ef0a090a868d |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 𝒯(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 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.http://dx.doi.org/10.1155/2009/780287 |
| spellingShingle | F. Albiac C. Leránoz The Tsirelson Space 𝒯(p) Has a Unique Unconditional Basis up to Permutation for 0<p<1 Abstract and Applied Analysis |
| title | The Tsirelson Space 𝒯(p) Has a Unique Unconditional Basis up to Permutation for 0<p<1 |
| title_full | The Tsirelson Space 𝒯(p) Has a Unique Unconditional Basis up to Permutation for 0<p<1 |
| title_fullStr | The Tsirelson Space 𝒯(p) Has a Unique Unconditional Basis up to Permutation for 0<p<1 |
| title_full_unstemmed | The Tsirelson Space 𝒯(p) Has a Unique Unconditional Basis up to Permutation for 0<p<1 |
| title_short | The Tsirelson Space 𝒯(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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