Dual Action on a von Neumann Algebra and Takesaki's Duality for a Locally Compact Group

Abstract

We define a dual action β of a locally compact group G on a von Neumann algebra N and a crossed dual product [formula omitted]. Then the Takesaki's duality is generalized in terms of these definitions as follows: [formula omitted], where [formula omitted] is the dual action dual to a given action [formula omitted], and [formula omitted], where [formula omitted] is the action dual to a given dual action [formula omitted]. As an application [formula omitted] whenever [formula omitted]. © 1977, Research Institute for Mathematical Sciences. All rights reserved.