Proceedings of the American Mathematical Society

Author(s): Razvan Anisca
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 46B20; Secondary 46B15
Posted: October 30, 2009
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Abstract: This paper complements a recent result of Dilworth, Ferenczi, Kutzarova and Odell regarding the ergodicity of strongly asymptotic $\ell_p$ spaces. We state this result in a more general form, involving domination relations, and we show that every asymptotically Hilbertian space which is not isomorphic to $\ell_2$ is ergodic. In particular, every weak Hilbert space which is not isomorphic to $\ell_2$ must be ergodic. Throughout the paper we construct explicitly the maps which establish the fact that the relation

is Borel reducible to isomorphism between subspaces of the Banach spaces involved.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46B20, 46B15

Razvan Anisca
Affiliation: Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, P7B 5E1, Canada
Email: ranisca@lakeheadu.ca

DOI: 10.1090/S0002-9939-09-10164-8
PII: S 0002-9939(09)10164-8
Received by editor(s): May 29, 2009,
Received by editor(s) in revised form: August 5, 2009
Posted: October 30, 2009
Additional Notes: The author was supported in part by NSERC Grant 312594-05
Communicated by: Nigel J. Kalton
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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