Locally Convex Quasi *-Algebras and their Representations

This book offers a review of the theory of locally convex quasi -algebras, authored by two of its contributors over the last 25 years. Quasi -algebras are partial algebraic structures that are motivated by certain applications in Mathematical Physics. They arise in a natural way by completing a -algebra under a locally convex -algebra topology, with respect to which the multiplication is separately continuous. Among other things, the book presents an unbounded representation theory of quasi -algebras, together with an analysis of normed quasi -algebras, their spectral theory and a study of the structure of locally convex quasi -algebras. Special attention is given to the case where the locally convex quasi -algebra is obtained by completing a C -algebra under a locally convex -algebra topology, coarser than the C -topology. Introducing the subject to graduate students and researchers wishing to build on their knowledge of the usual theory of Banach and/or locally convex algebras, this approach is supported by basic results and a wide variety of examples.