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A classification of Tsirelson type spaces | Jordi Lopez Abad
; Antonis Manoussakis
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19 Oct 2005 | Subject: | Functional Analysis; Logic | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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