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A strong generic ergodicity property of unitary and self-adjoint operators

Kechris, A. S. and Sofronidis, N. E. (2001) A strong generic ergodicity property of unitary and self-adjoint operators. Ergodic Theory and Dynamical Systems, 21 . pp. 1459-1479. ISSN 0143-3857. https://resolver.caltech.edu/CaltechAUTHORS:20111104-093324189

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Abstract

Consider the conjugacy action of the unitary group of an infinite-dimensional separable Hilbert space on the unitary operators. A strong generic ergodicity property of this action is established, by showing that any conjugacy invariants assigned in a definable way to unitary operators, and taking as values countable structures up to isomorphism, generically trivialize. Similar results are proved for conjugacy of self-adjoint operators and for measure equivalence. The proofs make use of the theory of turbulence for continuous actions of Polish groups, developed by Hjorth. These methods are also used to give a new solution to a problem of Mauldin in measure theory, by showing that any analytic set of pairwise orthogonal measures on the Cantor space is orthogonal to a product measure.


Item Type:Article
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http://dx.doi.org/10.1017/S0143385701001705 DOIUNSPECIFIED
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=86123PublisherUNSPECIFIED
Additional Information:© 2001 Cambridge University Press. Received 11 June 1999 and accepted in revised form 14 August 2000. Published online: 02 October 2001. We would like to acknowledge the support of NSF through grant DMS 9619880. We would also like to thank Tom Wolff for suggesting the argument in the proof of Proposition 5.6(i)(a).
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NSFDMS 9619880
Record Number:CaltechAUTHORS:20111104-093324189
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20111104-093324189
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27624
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:04 Nov 2011 20:12
Last Modified:03 Oct 2019 03:25

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