Partial *- Algebras and Their Operator Realizations

By I. Inoue, Jean-Pierre Antoine, C. Trapani

Book Overview

Algebras of bounded operators are familiar, either as C*-algebras or as von Neumann algebras. A first generalization is the notion of algebras of unbounded operators (O*-algebras), mostly developed by the Leipzig school and in Japan (for a review, we refer to the monographs of K. Schm dgen 1990] and A. Inoue 1998]). This volume goes one step further, by considering systematically partial *-algebras of unbounded operators (partial O*-algebras) and the underlying algebraic structure, namely, partial *-algebras. It is the first textbook on this topic. The first part is devoted to partial O*-algebras, basic properties, examples, topologies on them. The climax is the generalization to this new framework of the celebrated modular theory of Tomita-Takesaki, one of the cornerstones for the applications to statistical physics. The second part focuses on abstract partial *-algebras and their representation theory, obtaining again generalizations of familiar theorems (Radon-Nikodym, Lebesgue).

• Format: Hardcover
• Language: English
• ISBN: 1402010257
• ISBN13: 9781402010255
• Release Date: December 2002
• Publisher: Springer
• Length: 522 Pages
• Weight: 2.38 lbs.
• Dimensions: 1.1" x 6.6" x 9.7"