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Hypercyclic and mixing operator semigroups

Part of: Ergodic theory General theory of linear operators

Published online by Cambridge University Press:  27 June 2011

Stanislav Shkarin
Stanislav Shkarin
Affiliation:
Department of Pure Mathematics, Queen's University Belfast, University Road, Belfast BT7 1NN, UK ([email protected])
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Abstract

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We describe a class of topological vector spaces admitting a mixing uniformly continuous operator group with holomorphic dependence on the parameter t. This result builds on those existing in the literature. We also describe a class of topological vector spaces admitting no supercyclic strongly continuous operator semigroups .

Keywords

hypercyclic operatorssupercyclic operatorshypercyclic semigroupsmixing semigroups

MSC classification

Secondary: 47A16: Cyclic vectors, hypercyclic and chaotic operators 37A25: Ergodicity, mixing, rates of mixing
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 3 , October 2011 , pp. 761 - 782
Copyright
Copyright © Edinburgh Mathematical Society 2011

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