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Modified Mixed Tsirelson Spaces

✍ Scribed by S.A Argyros; I Deliyanni; D.N Kutzarova; A Manoussakis

Book ID
102972597
Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
820 KB
Volume
159
Category
Article
ISSN
0022-1236

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✦ Synopsis

We study the modified and boundedly modified mixed Tsirelson spaces

respectively, defined by a subsequence (F k n ) of the sequence of Schreier families (F n ). These are reflexive asymptotic l 1 spaces with an unconditional basis (e i ) i having the property that every sequence

are totally incomparable by proving that c 0 is finitely disjointly representable in every block subspace of T [(F n , % n ) n=1 ]. Next, we present an example of a boundedly modified mixed Tsirelson space X M(1), u =T M(1) [(F k n , % n ) n=1 ] which is arbitrarily distortable. Finally, we construct a variation of the space X M(1), u which is hereditarily indecomposable.

πŸ“œ SIMILAR VOLUMES

Distorting mixed tsirelson spaces
Distorting mixed tsirelson spaces
✍ G. Androulakis; E. Odell πŸ“‚ Article πŸ“… 1999 πŸ› The Hebrew University Magnes Press 🌐 English βš– 938 KB
Quasiminimality in mixed Tsirelson space
Quasiminimality in mixed Tsirelson spaces
✍ Antonis Manoussakis; Anna Maria Pelczar πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 280 KB

## Abstract We prove quasiminimality of regular the mixed Tsirelson spaces \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$T[(\mathcal {S}\_{n},\theta \_{n})\_{n}]$\end{document} with the sequence \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{emp