Regular subspaces of a Bourgain-Delbaen space $\mathscr B_{mT}$
| Autor: | Świętek, Michał |
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| Rok vydání: | 2017 |
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| Druh dokumentu: | Working Paper |
| Popis: | The space $\mathscr B_{mt}[(m_j)_j,(n_j)_j]$ is a Bourgain-Delbaen space modelled on a mixed Tsirelson space $T[(m_j)_j,(n_j)_j]$ and is a slight modification of $\mathfrak B_{\text{mt}}[(m_j)_j,(n_j)_j]$, a space defined by S. Argyros and R. Haydon. We prove that in every infinite dimensional subspace of $\mathscr B_{mt}[(m_j)_j,(n_j)_j]$ there exists a basic sequence equivalent to a sequence of weighted basis averages of increasing length from $T[(m_j)_j,(n_j)_j]$. We remark that the same is true for the original space $\mathfrak B_{\text{mt}}[(m_j)_j,(n_j)_j]$. Comment: 23 pages |
| Databáze: | arXiv |
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