A universal hypercyclic representation

Eli Glasner; Benjamin Weiss

doi:10.1016/j.jfa.2015.02.002

A universal hypercyclic representation

Eli Glasner^*, Benjamin Weiss

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

For any countable group, and also for any locally compact second countable, compactly generated topological group, G, we show the existence of a "universal" hypercyclic (i.e. topologically transitive) representation on a Hilbert space, in the sense that it simultaneously models every possible ergodic probability measure preserving free action of G.

Original language	English
Pages (from-to)	3478-3491
Number of pages	14
Journal	Journal of Functional Analysis
Volume	268
Issue number	11
DOIs	https://doi.org/10.1016/j.jfa.2015.02.002
State	Published - 1 Jun 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.

Keywords

Compactly generated groups
Ergodic system
Frequently hypercyclic
Universal linear system

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10.1016/j.jfa.2015.02.002

Cite this

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AB - For any countable group, and also for any locally compact second countable, compactly generated topological group, G, we show the existence of a "universal" hypercyclic (i.e. topologically transitive) representation on a Hilbert space, in the sense that it simultaneously models every possible ergodic probability measure preserving free action of G.

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KW - Ergodic system

KW - Frequently hypercyclic

KW - Universal linear system

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A universal hypercyclic representation

Abstract

Bibliographical note

Keywords

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