Partial *- Algebras and Their Operator Realizations: 553 (Mathematics and Its Applications, 553) - Softcover

Antoine, J-P; Inoue, I.; Trapani, C.

 
9789048161768: Partial *- Algebras and Their Operator Realizations: 553 (Mathematics and Its Applications, 553)

Synopsis

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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9781402010255: Partial *- Algebras and Their Operator Realizations: 553 (Mathematics and Its Applications, 553)

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ISBN 10:  1402010257 ISBN 13:  9781402010255
Publisher: Springer, 2002
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