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

Author(s): Anna Maria Pelczar
Journal: Proc. Amer. Math. Soc. 135 (2007), 1365-1375.
MSC (2000): Primary 46B03
Posted: October 27, 2006
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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.

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Additional Information:

Anna Maria Pelczar
Affiliation: Institute of Mathematics, Jagiellonian University, Kraków, Poland
Email: anna.pelczar@im.uj.edu.pl

DOI: 10.1090/S0002-9939-06-08599-6
PII: S 0002-9939(06)08599-6
Keywords: Tsirelson-type spaces, distortion
Received by editor(s): September 6, 2005
Received by editor(s) in revised form: November 16, 2005 and November 22, 2005
Posted: October 27, 2006
Communicated by: N. Tomczak-Jaegermann
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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