CROSSED PRODUCTS OF DUAL OPERATOR SPACES AND A CHARACTERIZATION OF GROUPS WITH THE APPROXIMATION PROPERTY

Abstract

Let G be a locally compact group. We prove that every L∞(G)- comodule is nondegenerate and saturated, whereas every L(G)-comodule is nondegenerate if and only if every L(G)-comodule is saturated if and only if G has the approximation property of Haagerup and Kraus. This allows us to extend known results from the duality theory of crossed products of von Neumann algebras to the recent theory of crossed products of dual operator spaces. Also, we obtain a characterization of groups with the approximation property involving crossed products improving a recent result of Crann and Neufang and we generalize a theorem of Anoussis, Katavolos and Todorov providing a less technical proof of it. © Copyright by THETA, 202

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