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Mixing operators with prescribed unimodular eigenvalues

Published online by Cambridge University Press:  28 December 2020

H.-P. BEISE
Affiliation:
Fachbereich Informatik, Hochschule Trier, D-54293Trier, Germany (e-mail:[email protected])
L. FRERICK
Affiliation:
Fachbereich IV Mathematik, Universität Trier, D-54286Trier, Germany (e-mail:[email protected])
J. MÜLLER*
Affiliation:
Fachbereich IV Mathematik, Universität Trier, D-54286Trier, Germany (e-mail:[email protected])

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.

Type
Original Article
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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