Operator Algebras in Dynamical Systems

This book is essential reading for graduate students and professionals working in operator algebras, mathematical physics and functional analysis.

Sh?ichir? Sakai (Author)

9780521400961, Cambridge University Press

Hardback, published 30 August 1991

232 pages
24.3 x 16.4 x 1.9 cm, 0.524 kg

"...makes for pleasant browsing and really worthwhile reading....This volume is a gem!" Richard V. Kadison, Bulletin of the American Mathematical Society

This book is concerned with the theory of unbounded derivations in C*-algebras, a subject whose study was motivated by questions in quantum physics and statistical mechanics, and to which the author has made a considerable contribution. This is an active area of research, and one of the most ambitious aims of the theory is to develop quantum statistical mechanics within the framework of the C*-theory. The presentation, which is based on lectures given in Newcastle upon Tyne and Copenhagen, concentrates on topics involving quantum statistical mechanics and differentiations on manifolds. One of the goals is to formulate the absence theorem of phase transitions in its most general form within the C* setting. For the first time, he globally constructs, within that setting, derivations for a fairly wide class of interacting models, and presents a new axiomatic treatment of the construction of time evolutions and KMS states.

Preface
1. Preliminaries
2. Bounded derivations
3. Unbounded derivations
4. C*-dynamical systems
Index.

Subject Areas: Calculus & mathematical analysis [PBK]