Stabilization of Tsirelson-type norms on $\ell _p$ spaces
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- by Anna Maria Pelczar PDF
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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.References
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Additional Information
- Anna Maria Pelczar
- Affiliation: Institute of Mathematics, Jagiellonian University, Kraków, Poland
- Email: anna.pelczar@im.uj.edu.pl
- Received by editor(s): September 6, 2005
- Received by editor(s) in revised form: November 16, 2005, and November 22, 2005
- Published electronically: October 27, 2006
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1365-1375
- MSC (2000): Primary 46B03
- DOI: https://doi.org/10.1090/S0002-9939-06-08599-6
- MathSciNet review: 2276645