Continuous Crossed Products and Type III Von Neumann Algebras

The theory of von Neumann algebras has undergone rapid development since the work of Tonita, Takesaki and Conner. These notes, based on lectures given at the University of Newcastle upon Tyne, provide an introduction to the subject and demonstrate the important role of the theory of crossed products. Part I deals with general continuous crossed products and proves the commutation theorem and the duality theorem. Part II discusses the structure of Type III von Neumann algebras and considers crossed products with modular actions. Restricting the treatment to the case of o-finite von Neumann algebras enables the author to work with faithful normal states.