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Mixing operators with prescribed unimodular eigenvalues

Part of: Ergodic theory General theory of linear operators Miscellaneous topics of analysis in the complex domain

Published online by Cambridge University Press:  28 December 2020

H.-P. BEISE ,
L. FRERICK  and
J. MÜLLER Open the ORCID record for J. MÜLLER [Opens in a new window]
H.-P. BEISE
Affiliation:
Fachbereich Informatik, Hochschule Trier, D-54293Trier, Germany (e-mail:H.Beise@inf.hochschule-trier.de)
L. FRERICK
Affiliation:
Fachbereich IV Mathematik, Universität Trier, D-54286Trier, Germany (e-mail:frerick@uni-trier.de)
J. MÜLLER*
Affiliation:
Fachbereich IV Mathematik, Universität Trier, D-54286Trier, Germany (e-mail:frerick@uni-trier.de)
*
e-mail:jmueller@uni-trier.de
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Abstract

For arbitrary closed countable subsets Z of the unit circle examples of topologically mixing operators on Hilbert spaces are given which have a densely spanning set of eigenvectors with unimodular eigenvalues restricted to Z. In particular, these operators cannot be ergodic in the Gaussian sense.

Keywords

Taylor shiftunimodular eigenvaluesmixing operatorrational approximation

MSC classification

Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators
Secondary: 30E10: Approximation in the complex domain 37A25: Ergodicity, mixing, rates of mixing
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 1 , January 2022 , pp. 1 - 8
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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