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The Haagerup property for groups and for tracial von Neumann algebras in terms of invariant and mixing states
The aim of the article is to provide characterizations of the Haagerup property for locally compact, second countable groups in terms of approximations of some non-ergodic invariant states by mixing ones for actions on unital $C^*$-algebras one the one hand, and for pairs of tracial von Neumann alge
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