Intermediate subalgebras and bimodules for general crossed products of von Neumann algebras
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© 2016 World Scientific Publishing. Let G be a discrete group acting on a von Neumann algebra M by properly outer ∗-automorphisms. In this paper, we study the containment M ⊆ M ⋊ α G of M inside the crossed product. We characterize the intermediate von Neumann algebras, extending earlier work of other authors in the factor case. We also determine the M-bimodules that are closed in the Bures topology and which coincide with the w∗-closed ones under a mild hypothesis on G. We use these results to obtain a general version of Mercer's theorem concerning the extension of certain isometric w∗-continuous maps on M-bimodules to ∗-automorphisms of the containing von Neumann algebras.
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Cameron, J. M., & Smith, R. R.
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Cameron, Jan M||Smith, Roger R
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Bimodule
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Crossed Product
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Von Neumann Algebra
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