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The ergodicity of weak Hilbert spaces

Author: Razvan Anisca
Journal: Proc. Amer. Math. Soc. 138 (2010), 1405-1413
MSC (2010): Primary 46B20; Secondary 46B15
Published electronically: October 30, 2009
MathSciNet review: 2578532
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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 $ E_0$ is Borel reducible to isomorphism between subspaces of the Banach spaces involved.

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Additional Information

Razvan Anisca
Affiliation: Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, P7B 5E1, Canada

Received by editor(s): May 29, 2009
Received by editor(s) in revised form: August 5, 2009
Published electronically: October 30, 2009
Additional Notes: The author was supported in part by NSERC Grant 312594-05
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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