Minimality properties of Tsirelson type spaces

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

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

Studia Mathematica, Tome 187 (2008), p. 233-263 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 2008-01-01

Zbl 1160.46007

EUDML-ID : urn:eudml:doc:284482

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     title = {Minimality properties of Tsirelson type spaces},
     journal = {Studia Mathematica},
     volume = {187},
     year = {2008},
     pages = {233-263},
     zbl = {1160.46007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-3-3}
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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) pp. 233-263. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-3-3/