Minimality properties of Tsirelson type spaces

Denka Kutzarova; Denny H. Leung; Antonis Manoussakis; Wee Kee Tang

doi:10.4064/sm187-3-3

Minimality properties of Tsirelson type spaces

Denka Kutzarova, Denny H. Leung, Antonis Manoussakis, Wee Kee Tang

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	233-263
Number of pages	31
Journal	Studia Mathematica
Volume	187
Issue number	3
DOIs	https://doi.org/10.4064/sm187-3-3
State	Published - 2008

Keywords

Partly modified mixed Tsirelson spaces
Subsequential minimality

ASJC Scopus subject areas

General Mathematics

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10.4064/sm187-3-3

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AB - We study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis (ek) is said to be subsequentially minimal if for every normalized block basis (xk) of (ek), there is a further block basis (yk) of (x k) such that (yk) is equivalent to a subsequence of (ek). 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.

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Minimality properties of Tsirelson type spaces

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