Partial *-Algebras and Their Operator Realizations (Mathematics and Its Applications)

Description:

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).

subjects: Operator algebras,  Partial algebras,  Functional Analysis,  Science/Mathematics,  Geometry - Algebraic,  Algebraic Topology,  Theory Of Operators,  Mathematics,  Mathematical Analysis,  Algebra - Linear,  General,  Mathematics / Algebra / Linear,  Mathematics / Mathematical Analysis,  Medical-General,  Operator theory,  Global analysis (Mathematics),  Analysis,  Mathematics, general