The Bourgain ell ^1index 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^1index is \omega^\eta . This answers a question of Judd and Odell.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2001
 arXiv:
 arXiv:math/0110154
 Bibcode:
 2001math.....10154L
 Keywords:

 Functional Analysis;
 46B
 EPrint:
 25 pages