Modified Mixed Tsirelson Spaces

S. A. Argyros, I. Deliyanni, D. N. Kutzarova, A. Manoussakis

Research output: Contribution to journalArticlepeer-review

Abstract

We study the modified and boundedly modified mixed Tsirelson spacesTM[(Fknn) n=1] andTM(s)[(Fknn) n=1], respectively, defined by a subsequence (Fkn) of the sequence of Schreier families (Fn). These are reflexive asymptotic ℓ1spaces with an unconditional basis (ei)ihaving the property that every sequence {xi}ni=1of normalized disjointly supported vectors contained in eii=nis equivalent to the basis of ℓn1. We show that if limθ1/nn=1 then the spaceT[(Fnn)n=1] and its modified variationsTM[(Fnn) n=1] orTM(s)[(Fnn) n=1] are totally incomparable by proving thatc0is finitely disjointly representable in every block subspace ofT[(Fnn)n=1]. Next, we present an example of a boundedly modified mixed Tsirelson spaceXM(1),u=TM(1)[(Fknn)n=1] which is arbitrarily distortable. Finally, we construct a variation of the spaceXM(1),uwhich is hereditarily indecomposable.

Original languageEnglish (US)
Pages (from-to)43-109
Number of pages67
JournalJournal of Functional Analysis
Volume159
Issue number1
DOIs
StatePublished - Oct 20 1998
Externally publishedYes

ASJC Scopus subject areas

  • Analysis

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