Distorting mixed tsirelson spaces

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Any regular mixed Tsirelson space T (θ n , S n) I N for which θn θ n → 0, where θ = lim n θ 1/n n , is shown to be arbitrarily distortable. Certain asymptotic ℓ 1 constants for those and other mixed Tsirelson spaces are calculated. Also a combinatorial result on the Schreier families (S α) α<ω 1 is proved and an application is given to show that for every Banach space X with a basis (e i), the ...

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ژورنال

عنوان ژورنال: Israel Journal of Mathematics

سال: 1999

ISSN: 0021-2172,1565-8511

DOI: 10.1007/bf02775031