Amenable dynamical systems over locally compact groups
نویسندگان
چکیده
Abstract We establish several new characterizations of amenable $W^*$ - and $C^*$ -dynamical systems over arbitrary locally compact groups. In the -setting we show that amenability is equivalent to (1) a Reiter property (2) existence certain net completely positive Herz–Schur multipliers $(M,G,\alpha )$ converging point weak* identity $G\bar {\ltimes }M$ . -setting, prove $(A,G,\alpha an analogous multiplier approximation reduced crossed product $G\ltimes A$ , as well particular case weak Bédos Conti [On discrete twisted systems, Hilbert -modules regularity. Münster J. Math. 5 (2012), 183–208] (generalized setting). When $Z(A^{**})=Z(A)^{**}$ it follows 1-positive Exel Ng [Approximation -algebraic bundles. Proc. Cambridge Philos. Soc. 132 (3) (2002), 509–522]. particular, when $A=C_0(X)$ commutative, $(C_0(X),G,\alpha coincides with topological G -space $(G,X)$
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2021
ISSN: ['0143-3857', '1469-4417']
DOI: https://doi.org/10.1017/etds.2021.57