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Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/7E972790-3BB6-4DBE-B07D-487E4A292DBA | ||
| Year | 2004 | ||
| Type of Item | Peer-Reviewed Journal Publication | ||
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| Bibliographic Citation | A.Manousakis,"A note on certain equivalent norms on Tsirelson' s space,"Math. J. ,vol. 46 , no. 2,pp. 379-390.April. 2004.doi:10.1017/S0017089504001867 https://doi.org/10.1017/S0017089504001867 | ||
| Appears in Collections |
We prove that the norm $\Vert\,{\cdot}\,\Vert_{n}$ of the space $T[\mathcal{S}_{n},\theta]$ and the norm $\Vert\,{\cdot}\,\Vert_{n}^{M}$ of its modified version $T_{M}[\mathcal{S}_{n},\theta]$ are 3-equivalent. As a consequence, using the results of E. Odell and N. Tomczak-Jaegermann, we obtain that there exists a $K\,{<}\,\infty$ such that for all $n$, $\Vert\cdot\Vert_{n}^{M}$ does not $K-$ distort any subspace of Tsirelson's space $T$.
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