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Media type:
E-Article
Title:
Mixing operators and small subsets of the circle
Contributor:
Bayart, Frédéric;
Matheron, Étienne
Published:
Walter de Gruyter GmbH, 2016
Published in:
Journal für die reine und angewandte Mathematik (Crelles Journal), 2016 (2016) 715, Seite 75-123
Language:
English
DOI:
10.1515/crelle-2014-0002
ISSN:
0075-4102;
1435-5345
Origination:
Footnote:
Description:
Abstract We provide complete characterizations, on Banach spaces with cotype 2, of those linear operators which happen to be weakly mixing or strongly mixing transformationswith respect to some nondegenerate Gaussian measure. These characterizations involve two families of small subsets of the circle: the countable sets and theso-called sets of uniqueness for Fourier–Stieltjes series. The most interesting part, i.e. the sufficient conditions for weak and strong mixing, is valid on an arbitrary(complex, separable) Fréchet space.