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29 March 2024
 
  » arxiv » math/0510410

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A classification of Tsirelson type spaces
Jordi Lopez Abad ; Antonis Manoussakis ; PostScript ; PDF ; Other formats ;
Date 19 Oct 2005
Subject Functional Analysis; Logic
AbstractWe give a complete classification of mixed Tsirelson spaces T[(F\_i, theta\_i)\_{i=1}^r ] for finitely many pairs of given compact and hereditary families F\_i of finite sets of integers and 0<theta\_i<1 in terms of the Cantor-Bendixson indexes of the families F\_i, and theta\_i (0< i < r+1). We prove that there are unique countable ordinal alpha and 0<theta<1 such that every block sequence of T[(F\_i, theta\_i)\_{i=1}^r ] has a subsequence equivalent to a subsequence of the natural basis of the T(S\_{omega^alpha},theta). Finally, we give a complete criterion of comparison in between two of these mixed Tsirelson spaces.
Source arXiv, math/0510410
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