Geodesic
On total incomparability of mixed Tsirelson spaces
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 4, pp. 841-859.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 46B03, 46B20
Keywords: mixed Tsirelson spaces; totally incomparable spaces 
@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/}
}
TY  - JOUR
AU  - Bernués, Julio
AU  - Pascual, Javier
TI  - On total incomparability of mixed Tsirelson spaces
JO  - Czechoslovak Mathematical Journal
PY  - 2003
SP  - 841
EP  - 859
VL  - 53
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2003__53_4_a5/
LA  - en
ID  - CMJ_2003__53_4_a5
ER  - 
%0 Journal Article
%A Bernués, Julio
%A Pascual, Javier
%T On total incomparability of mixed Tsirelson spaces
%J Czechoslovak Mathematical Journal
%D 2003
%P 841-859
%V 53
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2003__53_4_a5/
%G en
%F 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/