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Families of Finite Subsets of ℕ of Low Complexity and Tsirelson Type Spaces

✍ Scribed by Julio Bernués; Irene Deliyanni

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 229 KB
Volume: 222
Category: Article
ISSN: 0025-584X
DOI: 10.1002/1522-2616(200102)222:1<15::aid-mana15>3.0.co;2-2

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✦ Synopsis

We study Tsirelson type spaces of the form T (M k , θ k ) k=1 defined by a finite sequence (M k ) k=1 of compact families of finite subsets of IN. Using an appropriate index, denoted by i(M), to measure the complexity of a family M, we prove the following: If i(M k ) < ω for all k = 1, . . . , , then the space T (M k , θ k ) k=1 contains isomorphically some p, 1 < p < ∞, or c 0 . If i(M) = ω, then the space T [M, θ] contains a subspace isomorphic to a subspace of the original Tsirelson's space.

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