Title: Partial *-algebras and their operator realizations
First published: 2002
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
LC classification: QA251 .A55 2002