Antoine / Inoue / Trapani Partial *- Algebras and Their Operator Realizations

2002
ISBN: 978-94-017-0065-8
Verlag: Springer Netherland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 553, 522 Seiten, eBook

Reihe: Mathematics and Its Applications

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).

Zielgruppe

Research

Autoren/Hrsg.

Antoine, J-P

Inoue, I.

Trapani, C.

Inhaltsverzeichnis

Foreword. Introduction. 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 X>*-Representations. 9. Biweights on Partial *-Algebras. 10. Quasi *-Algebras of Operators in Rigged Hilbert Spaces. 11. Physical Applications. Outcome. Bibliography. Index.