Annals of Functional Analysis

Doubly stochastic operators with zero entropy

Bartosz Frej and Dawid Huczek

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Abstract

We study doubly stochastic operators with zero entropy. We generalize three famous theorems: Rokhlin’s theorem on genericity of zero entropy, Kushnirenko’s theorem on equivalence of discrete spectrum and nullity, and Halmos–von Neumann’s theorem on representation of maps with discrete spectrum as group rotations.

Article information

Source
Ann. Funct. Anal., Volume 10, Number 1 (2019), 144-156.

Dates
Received: 20 March 2018
Accepted: 22 June 2018
First available in Project Euclid: 16 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.afa/1547629230

Digital Object Identifier
doi:10.1215/20088752-2018-0015

Mathematical Reviews number (MathSciNet)
MR3899963

Zentralblatt MATH identifier
07045492

Subjects
Primary: 37A30: Ergodic theorems, spectral theory, Markov operators {For operator ergodic theory, see mainly 47A35}
Secondary: 28D20: Entropy and other invariants 47A35: Ergodic theory [See also 28Dxx, 37Axx]

Keywords
Markov operator entropy discrete spectrum Kushnirenko’s theorem Halmos–von Neumann’s theorem

Citation

Frej, Bartosz; Huczek, Dawid. Doubly stochastic operators with zero entropy. Ann. Funct. Anal. 10 (2019), no. 1, 144--156. doi:10.1215/20088752-2018-0015. https://projecteuclid.org/euclid.afa/1547629230


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References

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