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

Pelczar, Anna

doi:10.1090/S0002-9939-06-08599-6

Stabilization of Tsirelson-type norms on $\ell _p$ spaces
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by Anna Maria Pelczar PDF

Proc. Amer. Math. Soc. 135 (2007), 1365-1375 Request permission

Abstract:

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

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