| Dewey Class |
515 |
| Title |
Partial *-Algebras and Their Operator Realizations ([EBook]) / by Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani. |
| Author |
Antoine, Jean-Pierre |
| Added Personal Name |
Inoue, Atsushi. , 1944- author. |
| Trapani, Camillo |
| Other name(s) |
SpringerLink (Online service) |
| Publication |
Dordrecht : Springer Netherlands , 2002. |
| Physical Details |
XX, 522 pages : online resource. |
| Series |
Mathematics and its applications ; 553 |
| ISBN |
9789401700658 |
| Summary Note |
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).: |
| Contents note |
I Theory of Partial O*-Algebras -- 1 Unbounded Linear Operators in Hilbert Spaces -- 2 Partial O*-Algebras -- 3 Commutative Partial O*-Algebras -- 4 Topologies on Partial O*-Algebras -- 5 Tomita—Takesaki Theory in Partial O*-Algebras -- II Theory of Partial *-Algebras -- 6 Partial *-Algebras -- 7 *-Representations of Partial *-Algebras -- 8 Well-behaved *-Representations -- 9 Biweights on Partial *-Algebras -- 10 Quasi *-Algebras of Operators in Rigged Hilbert Spaces -- 11 Physical Applications -- Outcome. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) |
| Internet Site |
http://dx.doi.org/10.1007/978-94-017-0065-8 |
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