Ergodic invariant states and irreducible representations of crossed product C*-algebras

Huichi Huang, Jianchao Wu

Research output: Contribution to journalArticle

Abstract

Motivated by reformulating Furstenberg's ×p,×q conjecture via representations of a crossed product C*-algebra, we show that in a discrete C*-dynamical system (A, Γ), the space of (ergodic) Γ-invariant states on A is homeomorphic to a subspace of (pure) state space of A ⋊ Γ. Various applications of this in topological dynamical systems and representation theory are obtained.

Original languageEnglish (US)
Pages (from-to)159-172
Number of pages14
JournalJournal of Operator Theory
Volume78
Issue number1
DOIs
StatePublished - Jun 1 2017

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C*-dynamical System
Pure State
Crossed Product
Homeomorphic
Systems Theory
Representation Theory
Irreducible Representation
C*-algebra
State Space
Dynamical system
Subspace
Invariant

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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Ergodic invariant states and irreducible representations of crossed product C*-algebras. / Huang, Huichi; Wu, Jianchao.

In: Journal of Operator Theory, Vol. 78, No. 1, 01.06.2017, p. 159-172.

Research output: Contribution to journalArticle

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