
Partial *- Algebras and Their Operator Realizations
Kluwer Academic Publishers
1st Edition
Published on 31. December 2002
Book
Hardback
XX, 522 pages
978-1-4020-1025-5 (ISBN)
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. 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).
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).
More details
Series
Language
English
Place of publication
Dordrecht
Netherlands
Target group
Professional and scholarly
Research
Illustrations
XX, 522 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 35 mm
Weight
978 gr
ISBN-13
978-1-4020-1025-5 (9781402010255)
DOI
10.1007/978-94-017-0065-8
Schweitzer Classification
Other editions
Additional editions

J-P Antoine | I. Inoue | C. Trapani
Partial *- Algebras and Their Operator Realizations
Book
12/2010
Springer
€53.49
Shipment within 15-20 days
Content
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.