The Bourgain ell ^1-index of mixed Tsirelson space
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 (\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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- October 2001
- DOI:
- 10.48550/arXiv.math/0110154
- arXiv:
- arXiv:math/0110154
- Bibcode:
- 2001math.....10154L
- Keywords:
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- Functional Analysis;
- 46B
- E-Print:
- 25 pages