The Bourgain ell ^1-index of mixed Tsirelson space

Details The Bourgain ell ^1-index of mixed Tsirelson space The Bourgain ell ^1-index of mixed Tsirelson space

2001-10-15

arxiv.org/abs/math/0110154v1

Mathematics

Functional Analysis

25 pages

Scientific paper

Suppose that (F_n)_{n=0}^{\infty} is a sequence of regular families of finite subsets of N such that F_0 contains all singletons, and (\theta _n)_{n=1}^{\infty} is a nonincreasing null sequence in (0,1). In this paper, we compute the Bourgain \ell^1 - index of the mixed Tsirelson space T(F_0,(\theta_n, F_n)_{n=1}^{\infty}). As a consequence, it is shown that if \eta is a countable ordinal not of the form \omega^\xi for some limit ordinal \xi, then there is a Banach space whose \ell^1-index is \omega^\eta . This answers a question of Judd and Odell.

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