Partial *- Algebras and Their Operator Realizations

Partial *- Algebras and Their Operator Realizations

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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_-al...