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).
| Autorius: | J-P Antoine, C. Trapani, I. Inoue, |
| Serija: | Mathematics and Its Applications |
| Leidėjas: | Springer Netherlands |
| Išleidimo metai: | 2010 |
| Knygos puslapių skaičius: | 544 |
| ISBN-10: | 9048161762 |
| ISBN-13: | 9789048161768 |
| Formatas: | Knyga minkštu viršeliu |
| Kalba: | Anglų |
| Žanras: | Functional analysis and transforms |
Parašykite atsiliepimą apie „Partial *- Algebras and Their Operator Realizations“
