Partial *- Algebras and Their Operator Realizations: 553 (Mathematics and Its Applications, 553) - Hardcover

Antoine, J-P; Inoue, I.; Trapani, C.

Hardcover

ISBN 10: 1402010257 ISBN 13: 9781402010255

Publisher: Springer, 2002

Synopsis

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. Schmüdgen [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).

Edition details

• Publisher: Springer
• Publication date: 2002
• Language: English
• ISBN 10: 1402010257
• ISBN 13: 9781402010255
• Binding: Hardcover
• Number of pages: 542