Bimodules in crossed products of von Neumann algebras
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2015 Elsevier Inc. In this paper, we study bimodules over a von Neumann algebra M in the context of an inclusion MM *G, where G is a discrete group acting on a factor M by outer *-automorphisms. We characterize the M-bimodules XM*G that are closed in the Bures topology in terms of the subsets of G. We show that this characterization also holds for w*-closed bimodules when G has the approximation property (AP), a class of groups that includes all amenable and weakly amenable ones. As an application, we prove a version of Mercer's extension theorem for certain w*-continuous surjective isometric maps on X.