1Institute of Mathematics Bulgarian Academy of Sciences and Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL 61801, U.S.A. 2Department of Mathematics National University of Singapore 2 Science Drive 2 Singapore 117543 3Department of Mathematics University of Aegean Karlovasi, Samos, GR 83200, Greece 4Mathematics 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
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.
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
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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author = {Denka Kutzarova and Denny H. Leung and Antonis Manoussakis and Wee-Kee Tang},
title = {Minimality properties of {Tsirelson} type spaces},
journal = {Studia Mathematica},
pages = {233--263},
year = {2008},
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doi = {10.4064/sm187-3-3},
language = {en},
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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
