Abstract of a paper by Denka Kutzarova, Denny Leung, Antonis Manoussakis and Wee Kee Tang
This is an announcement for the paper "Minimality properties of Tsirelson type spaces" by Denka Kutzarova, Denny Leung, Antonis Manoussakis and Wee Kee Tang. Abstract: In this paper, 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 (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. Archive classification: Functional Analysis The source file(s), SubseqMinimal8A.tex: 107238 bytes, is(are) stored in gzipped form as 0702210.gz with size 27kb. The corresponding postcript file has gzipped size 176kb. Submitted from: matlhh@nus.edu.sg The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0702210 or http://arXiv.org/abs/math.FA/0702210 or by email in unzipped form by transmitting an empty message with subject line uget 0702210 or in gzipped form by using subject line get 0702210 to: math@arXiv.org.
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Dale Alspach