Partial *-algebras and their operator realizations /
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] an...
| Main Author: | |
|---|---|
| Corporate Author: | |
| Other Authors: | , |
| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht :
Springer,
2002.
|
| Series: | Mathematics and its applications (Kluwer Academic Publishers) ;
v. 553. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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). |
|---|---|
| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xx, 521 pages) |
| Bibliography: | Includes bibliographical references (pages [495]-516) and index. |
| ISBN: | 9789401700658 (electronic bk.) 9401700656 (electronic bk.) |