Minimality properties of Tsirelson type spaces

Denka Kutzarova, et al. "Minimality properties of Tsirelson type spaces." Studia Mathematica 187.3 (2008): 233-263. <http://eudml.org/doc/284482>.

@article{DenkaKutzarova2008,
abstract = {We study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis $(e_\{k\})$ is said to be subsequentially minimal if for every normalized block basis $(x_\{k\})$ of $(e_\{k\})$, there is a further block basis $(y_\{k\})$ of $(x_\{k\})$ such that $(y_\{k\})$ is equivalent to a subsequence of $(e_\{k\})$. Sufficient conditions are given for a partly modified mixed Tsirelson space to be subsequentially minimal, and connections with Bourgain’s ℓ¹-index are established. It is also shown that a large class of mixed Tsirelson spaces fails to be subsequentially minimal in a strong sense.},
author = {Denka Kutzarova, Denny H. Leung, Antonis Manoussakis, Wee-Kee Tang},
journal = {Studia Mathematica},
keywords = {subsequential minimality; partly modified mixed Tsirelson spaces; Bourgain’s -index; quasi-minimal spaces; - spreading models},
language = {eng},
number = {3},
pages = {233-263},
title = {Minimality properties of Tsirelson type spaces},
url = {http://eudml.org/doc/284482},
volume = {187},
year = {2008},
}

TY - JOUR
AU - Denka Kutzarova
AU - Denny H. Leung
AU - Antonis Manoussakis
AU - Wee-Kee Tang
TI - Minimality properties of Tsirelson type spaces
JO - Studia Mathematica
PY - 2008
VL - 187
IS - 3
SP - 233
EP - 263
AB - We study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis $(e_{k})$ is said to be subsequentially minimal if for every normalized block basis $(x_{k})$ of $(e_{k})$, there is a further block basis $(y_{k})$ of $(x_{k})$ such that $(y_{k})$ is equivalent to a subsequence of $(e_{k})$. Sufficient conditions are given for a partly modified mixed Tsirelson space to be subsequentially minimal, and connections with Bourgain’s ℓ¹-index are established. It is also shown that a large class of mixed Tsirelson spaces fails to be subsequentially minimal in a strong sense.
LA - eng
KW - subsequential minimality; partly modified mixed Tsirelson spaces; Bourgain’s -index; quasi-minimal spaces; - spreading models
UR - http://eudml.org/doc/284482
ER -