Partial *- Algebras and Their Operator Realizations by Jean-Pierre ANTOINEPartial *- Algebras and Their Operator Realizations by Jean-Pierre ANTOINE

Partial *- Algebras and Their Operator Realizations

byJean-Pierre ANTOINE, Atsushi Inoue, C. Trapani

Paperback | December 4, 2010

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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).
Title:Partial *- Algebras and Their Operator RealizationsFormat:PaperbackDimensions:541 pages, 9.25 × 6.1 × 0.03 inPublished:December 4, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048161762

ISBN - 13:9789048161768

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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.