Partial *- Algebras and Their Operator Realizations
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).

1101311496
Partial *- Algebras and Their Operator Realizations
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).

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Partial *- Algebras and Their Operator Realizations

Partial *- Algebras and Their Operator Realizations

Partial *- Algebras and Their Operator Realizations

Partial *- Algebras and Their Operator Realizations

Paperback(Softcover reprint of hardcover 1st ed. 2003)

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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. 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 , #553
Edition description: Softcover reprint of hardcover 1st ed. 2003
Pages: 522
Product dimensions: 6.10(w) x 9.25(h) x 0.04(d)

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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