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The Bourgain ell ^1-index of mixed Tsirelson space

Denny H. Leung·Wee-Kee Tang
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Abstract

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 (θ_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,(θ_n, F_n)_{n=1}^{\infty}). As a consequence, it is shown that if ηis a countable ordinal not of the form ω^ξfor some limit ordinal ξ, then there is a Banach space whose \ell^1-index is ω^η. This answers a question of Judd and Odell.

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Denny H. Leung, Wee-Kee Tang. 2001-10-15. The Bourgain ell ^1-index of mixed Tsirelson space. https://arxiv.org/abs/math/0110154

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