Recurrence and ergodicity in unital *-algebras

Details Recurrence and ergodicity in unital *-algebras Recurrence and ergodicity in unital *-algebras

2002-08-10

arxiv.org/abs/math/0208082v1

J. Math. Anal. Appl. 287, pp. 430-443 (2003)

Mathematics

Dynamical Systems

16 pages

Scientific paper

Results concerning recurrence and ergodicity are proved in an abstract Hilbert space setting based on the proof of Khintchine's recurrence theorem for sets, and on the Hilbert space characterization of ergodicity. These results are carried over to a non-commutative *-algebraic setting using the GNS-construction. This generalizes the corresponding measure theoretic results, in particular a variation of Khintchine's Theorem for ergodic systems, where the image of one set overlaps with another set, instead of with itself.

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