Continuous Crossed Products and Type III Von Neumann Algebras

These notes, based on lectures given at the University of Newcastle upon Tyne, provide an introduction to the theory of von Neumann algebras.

A. van Daele (Author)

9780521219754, Cambridge University Press

Paperback, published 20 July 1978

80 pages
22.8 x 15.2 x 0.5 cm, 0.125 kg

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.

Part I. Crossed products of von Neumann algebras: 1. Introduction
2. Crossed products of von Neumann algebras
3. The commutation theorem for crossed products
4. Duality
Part II. The structure of type III von Neumann algebras: 5. Introduction
6. Crossed products with modular actions
7. The semi-finiteness of M o R
8. The structure of type III von Neumann algebras.

Subject Areas: Algebra [PBF]