The ergodicity of weak Hilbert spaces

Anisca, Razvan

doi:10.1090/S0002-9939-09-10164-8

The ergodicity of weak Hilbert spaces
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Proc. Amer. Math. Soc. 138 (2010), 1405-1413 Request permission

Erratum: Proc. Amer. Math. Soc. 148 (2020), 3199-3201.

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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