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Recurrence and ergodicity in unital *-algebras

Rocco Duvenhage·Anton Stroh
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Abstract

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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Rocco Duvenhage, Anton Stroh. 2002-08-10. Recurrence and ergodicity in unital *-algebras. https://doi.org/10.1016/s0022-247x(02)00571-1

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