UNIQUE ERGODICITY OF FREE SHIFTS AND SOME OTHER AUTOMORPHISMS OF C-ALGEBRAS

A notion of unique ergodicity relative to the fixed-point subalgebra is defined for automorphisms of unital C*-algebras. It is proved that the free shift on any reduced amalgamated free product C*-algebra is uniquely ergodic relative to its fixed-point subalgebra, as are automorphisms of reduced gro...

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Bibliographic Details
Published in:Journal of operator theory 2009-03, Vol.61 (2), p.279-294
Main Authors: ABADIE, BEATRIZ, DYKEMA, KEN
Format: Article
Language:English
Subjects:
Automorphisms
Ergodic theory
Fixed point property
Integers
Mathematical inequalities
Mathematical theorems
Scalars
Subalgebras
Tensors
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Summary:A notion of unique ergodicity relative to the fixed-point subalgebra is defined for automorphisms of unital C*-algebras. It is proved that the free shift on any reduced amalgamated free product C*-algebra is uniquely ergodic relative to its fixed-point subalgebra, as are automorphisms of reduced group C*-algebras arising from certain automorphisms of groups. A generalization of Haagerup's inequality, yielding bounds on the norms of certain elements in reduced amalgamated free product C*-algebras, is proved.
ISSN:0379-4024
1841-7744