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## Minimality properties of Tsirelson type spaces

### Tom 187 / 2008

Studia Mathematica 187 (2008), 233-263 MSC: Primary 46B20; Secondary 46B45. DOI: 10.4064/sm187-3-3

#### Streszczenie

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 $\ell^{1}$-index are established. It is also shown that a large class of mixed Tsirelson spaces fails to be subsequentially minimal in a strong sense.

#### Autorzy

• Denka KutzarovaInstitute of Mathematics
and
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL 61801, U.S.A.
e-mail
• Denny H. LeungDepartment of Mathematics
National University of Singapore
2 Science Drive 2
Singapore 117543
e-mail
• Antonis ManoussakisDepartment of Mathematics
University of Aegean
Karlovasi, Samos, GR 83200, Greece
e-mail
• Wee-Kee TangMathematics and Mathematics Education
National Institute of Education
Nanyang Technological University
1 Nanyang Walk
Singapore 637616
e-mail

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