Bimodules in crossed products of von Neumann algebras Academic Article uri icon

abstract

  • © 2015 Elsevier Inc. In this paper, we study bimodules over a von Neumann algebra M in the context of an inclusion M⊂M *αG, where G is a discrete group acting on a factor M by outer *-automorphisms. We characterize the M-bimodules X⊂M*αG 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.

author list (cited authors)

  • Cameron, J., & Smith, R. R.

citation count

  • 5

complete list of authors

  • Cameron, Jan||Smith, Roger R

publication date

  • April 2015