Partial *- Algebras and Their Operator Realizations
Author:   J-P Antoine ,  I. Inoue ,  C. Trapani
Publisher:   Springer
Edition:   Softcover reprint of hardcover 1st ed. 2003
Volume:   553
ISBN:  

9789048161768


Pages:   522
Publication Date:   04 December 2010
Format:   Paperback
Availability:   Out of stock   Availability explained
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Partial *- Algebras and Their Operator Realizations


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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. Schmudgen [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).

Full Product Details

Author:   J-P Antoine ,  I. Inoue ,  C. Trapani
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of hardcover 1st ed. 2003
Volume:   553
Dimensions:   Width: 15.50cm , Height: 2.70cm , Length: 23.50cm
Weight:   0.825kg
ISBN:  

9789048161768


ISBN 10:   9048161762
Pages:   522
Publication Date:   04 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock   Availability explained
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

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.

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