Abstract
AbstractWe 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 = limnθ1/nn, 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 (θn)n the dual spaces are quasiminimal.
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