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Title: On total incomparability of mixed Tsirelson spaces (English)
Author: Bernués, Julio
Author: Pascual, Javier
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 53
Issue: 4
Year: 2003
Pages: 841-859
Summary lang: English
Category: math
Summary: We give criteria of total incomparability for certain classes of mixed Tsirelson spaces. We show that spaces of the form $T[(\mathcal M_k,\theta _k)_{k =1}^{l}]$ with index $i(\mathcal M_k)$ finite are either $c_0$ or $\ell _p$ saturated for some $p$ and we characterize when any two spaces of such a form are totally incomparable in terms of the index $i(\mathcal M_k)$ and the parameter $\theta _k$. Also, we give sufficient conditions of total incomparability for a particular class of spaces of the form $T[(\mathcal A_k,\theta _k)_{k = 1}^\infty ]$ in terms of the asymptotic behaviour of the sequence $\Bigl \Vert \sum _{i=1}^n e_i\Bigr \Vert $ where $(e_i)$ is the canonical basis. (English)
Keyword: mixed Tsirelson spaces
Keyword: totally incomparable spaces
MSC: 46B03
MSC: 46B20
idZBL: Zbl 1080.46507
idMR: MR2018834
Date available: 2009-09-24T11:07:07Z
Last updated: 2020-07-03
Stable URL:
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