This is an announcement for the paper "A classification of Tsirelson type spaces" by Jordi Lopez Abad and Antonis Manoussakis.

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.

Archive classification: Functional Analysis; Logic

Mathematics Subject Classification: MSC 46b20, 05d10

The source file(s), lop-man.tex: 131413 bytes, is(are) stored in gzipped form as 0510410.gz with size 37kb. The corresponding postcript file has gzipped size 150kb.

Submitted from: abad@logique.jussieu.fr

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