Quasiminimality in mixed Tsirelson spaces

TL;DR

This paper establishes quasiminimality properties of certain mixed Tsirelson spaces and their duals, providing new insights into their structural characteristics under specific conditions.

Contribution

It proves quasiminimality for a class of mixed Tsirelson spaces and their duals, extending understanding of their geometric and structural properties.

Findings

Quasiminimality of regular mixed Tsirelson spaces T[(S_n,θ_n)_n] established.

Quasiminimality of all mixed Tsirelson spaces T[(A_n,θ_n)_n] proven.

Dual spaces are quasiminimal under certain conditions on (θ_n)_n.

Abstract

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