Duals of Tirilman spaces have unique subsymmetric basic sequences

TL;DR

This paper proves that in the duals of Tirilman spaces, all subsymmetric basic sequences are equivalent to a specific canonical basis, highlighting a unique structural property of these dual spaces.

Contribution

It establishes that all subsymmetric basic sequences in the dual Tirilman spaces are equivalent to their canonical subsymmetric basis, revealing a distinctive feature of these dual spaces.

Findings

All subsymmetric basic sequences in $Ti^*(p,eta)$ are equivalent to the canonical basis.

The dual Tirilman spaces have a unique subsymmetric basis structure.

The canonical basis in the dual space is not symmetric.

Abstract

The Tirilman spaces $Ti(p,\gamma)$, $1<p<\infty$, were introduced by Casazza and Shura as variations of the spaces constructed by Tzafriri. We prove that all subsymmetric basic sequences in the dual space $Ti^*(p,\gamma)$ are equivalent to its canonical subsymmetic but not symmetric basis.