On total incomparability of mixed Tsirelson spaces
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 4, pp. 841-859
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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.
@article{CMJ_2003__53_4_a5,
author = {Bernu\'es, Julio and Pascual, Javier},
title = {On total incomparability of mixed {Tsirelson} spaces},
journal = {Czechoslovak Mathematical Journal},
pages = {841--859},
publisher = {mathdoc},
volume = {53},
number = {4},
year = {2003},
mrnumber = {2018834},
zbl = {1080.46507},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2003__53_4_a5/}
}
Bernués, Julio; Pascual, Javier. On total incomparability of mixed Tsirelson spaces. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 4, pp. 841-859. http://geodesic.mathdoc.fr/item/CMJ_2003__53_4_a5/