منابع مشابه
Distorting Mixed Tsirelson Spaces∗
Any regular mixed Tsirelson space T (θn, Sn)IN for which θn θn → 0, where θ = limn θ n , is shown to be arbitrarily distortable. Certain asymptotic `1 constants for those and other mixed Tsirelson spaces are calculated. Also a combinatorial result on the Schreier families (Sα)α<ω1 is proved and an application is given to show that for every Banach space X with a basis (ei), the two ∆-spectrums ...
متن کاملBanach Spaces of the Type of Tsirelson
Abstract . To any pair (M , θ ) , where M is a family of finite subsets of N , compact in the pointwise topology, and 0 < θ < 1 , we associate a Tsirelson-type Banach space T θ M . It is shown that if the Cantor-Bendixson index of M is greater than n and θ > 1 n then T θ M is reflexive. Moreover, if the Cantor-Bendixson index of M is greater than ω then T θ M does not contain any l , while if t...
متن کاملA Classification of Tsirelson Type Spaces
We give a complete classification of mixed Tsirelson spaces T [(Fi, θi) r i=1] for finitely many pairs of given compact and hereditary families Fi of finite sets of integers and 0 < θi < 1 in terms of the Cantor-Bendixson indexes of the families Fi, and θi (1 ≤ i ≤ r). We prove that there are unique countable ordinal α and 0 < θ < 1 such that every block sequence of T [(Fi, θi) r i=1] has a sub...
متن کاملMinimality Properties of Tsirelson Type Spaces
In this paper, we study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis (ek) is said to be subsequentially minimal if for every normalized block basis (xk) of (ek), there is a further block (yk) of (xk) such that (yk) is equivalent to a subsequence of (ek). Sufficient conditions are given for a partly modified mixed Tsirelson space to be s...
متن کاملTHE l-INDEX OF TSIRELSON TYPE SPACES
Let E be a separable Banach space not containing a copy of l. The complexity of the l(n)’s inside E may be measured by Bourgain’s l-index [3] or by locating so called lα-spreading models [8]. It is easy to see that the existence of l 1 α-spreading models implies a large l-index. In general, the implication is not reversible [7, Remark 6.6(i)]. However, suppose that T is the standard Tsirelson s...
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ژورنال
عنوان ژورنال: Mathematische Nachrichten
سال: 2013
ISSN: 0025-584X
DOI: 10.1002/mana.200810118