Operator Algebras in Dynamical Systems [Hardcover]

This book is essential reading for graduate students and professionals working in operator algebras, mathematical physics and functional analysis.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 presentation concentrates on topics involving quantum statistical mechanics and differentiations on manifolds.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 presentation concentrates on topics involving quantum statistical mechanics and differentiations on manifolds.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 considerable contributions. 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 C*-theory. The presentation 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, the author 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. The theory for the normal derivations is developed very clearly in this important book, and the subject is one of the most central ones in the modern theory of operator algebrlã