Intermediate subalgebras and bimodules for general crossed products of von Neumann algebras Academic Article uri icon

abstract

  • © 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.

author list (cited authors)

  • Cameron, J. M., & Smith, R. R.

citation count

  • 2

complete list of authors

  • Cameron, Jan M||Smith, Roger R

publication date

  • October 2016