| Partial *- Algebras and Their Operator Realizations 2003 Edition Contributor(s): Antoine, J-P (Author), Inoue, I. (Author), Trapani, C. (Author) |
|
 |
ISBN: 1402010257 ISBN-13: 9781402010255 Publisher: Springer OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: December 2002 |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - Linear - Medical - Mathematics | Mathematical Analysis |
| Dewey: 512.55 |
| LCCN: 2002041334 |
| Series: Mathematics and Its Applications |
| Physical Information: 1.11" H x 6.58" W x 9.7" (2.38 lbs) 522 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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). |