Stabilization of Tsirelson-type norms on $\ell_p$ spaces

Abstract

We consider classical Tsirelson-type norms of $T[A_r,θ]$ and their modified versions on $\ell_p$ spaces. We show that for any $1<p<\infty$ there is a constant $λ_p$ such that considered Tsirelson-type norms do not $λ_p$-distort any of subspaces of $\ell_p$.