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Partial -Algebras and Their Operator Realizations

Name: Partial -Algebras and Their Operator Realizations
Brand: Springer Netherlands
SKU: 01974586
Price: 51.36 EUR
Availability: InStock
Author: Jean-Pierre Antoine
ISBN: 9789048161768

Jean-Pierre Antoine

I. Inoue

C. Trapani

Language

English

Book Paperback

Libristo code: 01974586

Publishers Springer Netherlands, October 2010

Algebras of bounded operators are familiar, either as C -algebras or as von Neumann algebras. A firs... Full description

Libristo code: 01974586

125 b

51.36 €

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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).