The Bourgain ell 1-index of mixed Tsirelson space
Denny H. Leung, Wee-Kee Tang
Abstract
Suppose that (Fn)n=0∞ is a sequence of regular families of finite subsets of N such that F0 contains all singletons, and (θn)n=1∞ is a nonincreasing null sequence in (0,1). In this paper, we compute the Bourgain 1 - index of the mixed Tsirelson space T(F0,(θn, Fn)n=1∞). As a consequence, it is shown that if ηis a countable ordinal not of the form ωξfor some limit ordinal ξ, then there is a Banach space whose 1-index is ωη. This answers a question of Judd and Odell.
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