Quasiminimality in mixed Tsirelson spaces

Abstract

We prove quasiminimality of the regular mixed Tsirelson spaces T[(S_n,θ_n)_n] with the sequence (\frac{θ_n}{θ^n})_n decreasing, where θ=\lim_n θ_n^{1/n}, and quasiminimality of all mixed Tsirelson spaces T[(A_n,θ_n)_n]. We prove that under certain assumptions on the sequence (θ_n)_n the dual spaces are quasiminimal.

26 pages, assumptions of Theorem 4.10 revised, corrected typos