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.
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