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

abstract

• Let [Formula: see text] be a discrete group acting on a von Neumann algebra [Formula: see text] by properly outer -automorphisms. In this paper, we study the containment [Formula: see text] of [Formula: see text] 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 [Formula: see text]-bimodules that are closed in the Bures topology and which coincide with the [Formula: see text]-closed ones under a mild hypothesis on [Formula: see text]. We use these results to obtain a general version of Mercers theorem concerning the extension of certain isometric [Formula: see text]-continuous maps on [Formula: see text]-bimodules to -automorphisms of the containing von Neumann algebras.

authors

• Smith, Roger

published proceedings

• INTERNATIONAL JOURNAL OF MATHEMATICS

author list (cited authors)

• Cameron, J. M., & Smith, R. R.

citation count

• 4

complete list of authors

• Cameron, Jan M||Smith, Roger R

publication date

• October 2016

publisher

• World Scientific Publishing  Publisher

published in

• International Journal of Mathematics  Journal

keywords

• Bimodule
• Crossed Product
• Von Neumann Algebra

Digital Object Identifier (DOI)

• 10.1142/S0129167X16500919

start page

• 1650091

end page

• 1650091

volume

• 27

issue

• 11

URL

• http%3A%2F%2Fdx.doi.org%2F10.1142%2Fs0129167x16500919