Stabilization of Tsirelson-type norms on ℓ_{𝑝} spaces

Abstract

We consider classical Tsirelson-type norms of T [ A n , θ ] T[\mathcal {A}_n,\theta ] and their modified versions on ℓ p \ell _p spaces, 1 > p > ∞ 1>p>\infty . We show that the modified Tsirelson-type norms do not distort any of the subspaces of the ℓ p \ell _p spaces. We prove that Tsirelson-type norms, being equivalent to their modified versions, may at most 2-distort ℓ p \ell _p spaces.