On certain equivalent norms on Tsirelson's space

1998/04/09 by Edward Odell, Odell, Edward, Nicole Tomczak-Jaegermann +1
Mathematics · #46B03 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B03

paper · pdf · doi:10.48550/arxiv.math/9804057

19 pp., LaTeX

arxiv created 1998/04/09 · arxiv updated 2009/11/30

Abstract

Tsirelson's space T is known to be distortable but it is open as to whether or not T is arbitrarily distortable. For n∈ \Bbb N the norm ‖⋅‖_n of the Tsirelson space T(S_n,2^-n) is equivalent to the standard norm on T. We prove there exists K<∞ so that for all n, ‖⋅‖_n does not K distort any subspace Y of T.

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