Geodesic
Minimality properties of Tsirelson type spaces
Denka Kutzarova 1   ; Denny H. Leung 2   ; Antonis Manoussakis 3   ; Wee-Kee Tang 4
1 Institute of Mathematics Bulgarian Academy of Sciences and Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL 61801, U.S.A.
2 Department of Mathematics National University of Singapore 2 Science Drive 2 Singapore 117543
3 Department of Mathematics University of Aegean Karlovasi, Samos, GR 83200, Greece
4 Mathematics and Mathematics Education National Institute of Education Nanyang Technological University 1 Nanyang Walk Singapore 637616
Studia Mathematica, Tome 187 (2008) no. 3, pp. 233-263 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm187-3-3
Keywords: study minimality properties partly modified mixed tsirelson spaces banach space normalized basis said subsequentially minimal every normalized block basis there further block basis equivalent subsequence sufficient conditions given partly modified mixed tsirelson space subsequentially minimal connections bourgains ell index established shown large class mixed tsirelson spaces fails subsequentially minimal strong sense

Denka Kutzarova  1   ; Denny H. Leung  2   ; Antonis Manoussakis  3   ; Wee-Kee Tang  4

1 Institute of Mathematics Bulgarian Academy of Sciences and Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL 61801, U.S.A.
2 Department of Mathematics National University of Singapore 2 Science Drive 2 Singapore 117543
3 Department of Mathematics University of Aegean Karlovasi, Samos, GR 83200, Greece
4 Mathematics and Mathematics Education National Institute of Education Nanyang Technological University 1 Nanyang Walk Singapore 637616 
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     title = {Minimality properties of {Tsirelson} type spaces},
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Denka Kutzarova; Denny H. Leung; Antonis Manoussakis; Wee-Kee Tang. Minimality properties of Tsirelson type spaces. Studia Mathematica, Tome 187 (2008) no. 3, pp. 233-263. doi: 10.4064/sm187-3-3

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