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Title

Gaussian automorphisms whose ergodic self-joinings are Gaussian

Authors 1, 2, 3

Affiliations

  1. Department of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
  2. Laboratoire d'Analyse, Géométrie et Applications, UMR 7539, Université Paris-Nord & CNRS, Av. J.-B. Clément, 93430 Villetaneuse, France
  3. Laboratoire de Probabilités, URA CNRS, Université Paris 6, Tour 56, 4 Place Jussieu, 75230 Paris Cedex 05, France

Abstract

 We study ergodic properties of the class of Gaussian automorphisms whose ergodic self-joinings remain Gaussian. For such automorphisms we describe the structure of their factors and of their centralizer. We show that Gaussian automorphisms with simple spectrum belong to this class.  We prove a new sufficient condition for non-disjointness of automorphisms giving rise to a better understanding of Furstenberg's problem relating disjointness to the lack of common factors. This and an elaborate study of isomorphisms between classical factors of Gaussian automorphisms allow us to give a complete solution of the disjointness problem between a Gaussian automorphism whose ergodic self-joinings remain Gaussian and an arbitrary Gaussian automorphism.

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Fundamenta Mathematicae
2000/164/3
Export to PBN, Opens in new tab
Pages:
253-293
Main language of publication
English
Received
1999-09-23
Accepted
2000-03-30
Published
2000
Exact and natural sciences