Partial *- Algebras and Their Operator Realizations / Edition 1

Partial *- Algebras and Their Operator Realizations / Edition 1

by Jean-Pierre ANTOINE, Atsushi Inoue, C. Trapani
     
 

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ISBN-10: 9048161762

ISBN-13: 9789048161768

Pub. Date: 12/03/2010

Publisher: Springer Netherlands

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

Overview

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).

Product Details

ISBN-13:
9789048161768
Publisher:
Springer Netherlands
Publication date:
12/03/2010
Series:
Mathematics and Its Applications (closed), #553
Edition description:
Softcover reprint of hardcover 1st ed. 2003
Pages:
522
Product dimensions:
6.14(w) x 9.21(h) x 1.10(d)

Table of Contents

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.

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