Quasiminimality in mixed Tsirelson spaces

✍ Scribed by Antonis Manoussakis; Anna Maria Pelczar

• Book ID: 102495125
• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 280 KB
• Volume: 284
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200910845

✦ Synopsis

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{empty}$\big (\frac{\theta _n}{\theta ^n}\big )_n$\end{document} decreasing, where θ = lim~n~θ^1/n^~n~, and quasiminimality of all mixed Tsirelson spaces \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$T[(\mathcal {A}_{n},\theta _{n})_{n}]$\end{document}. We prove that under certain assumptions on the sequence (θ~n~)~n~ the dual spaces are quasiminimal.