Locally Convex Quasi *-Algebras and their Representations

1. Front Matter

   Pages i-vii

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2. Introduction

   • Maria Fragoulopoulou, Camillo Trapani

   Pages 1-7

3. Algebraic Aspects

   • Maria Fragoulopoulou, Camillo Trapani

   Pages 9-29

4. Normed Quasi *-Algebras: Basic Theory and Examples

   • Maria Fragoulopoulou, Camillo Trapani

   Pages 31-66

5. Normed Quasi *-Algebras: Bounded Elements and Spectrum

   • Maria Fragoulopoulou, Camillo Trapani

   Pages 67-94

6. CQ*-Algebras

   • Maria Fragoulopoulou, Camillo Trapani

   Pages 95-142

7. Locally Convex Quasi *-Algebras

   • Maria Fragoulopoulou, Camillo Trapani

   Pages 143-161

8. Locally Convex Quasi C*-Algebras and Their Structure

   • Maria Fragoulopoulou, Camillo Trapani

   Pages 163-200

9. Back Matter

   Pages 201-262

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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 usualtheory of Banach and/or locally convex algebras, this approach is supported by basic results and a wide variety of examples.

• Partial *-algebras
• Quasi *-algebras
• Representation Theory
• Spectral Theory
• Unbounded Operator Algebras

“The book under review is a fine work which enriches the literature of unbounded operator algebras and their representations. … the excellent organization of the material and the meticulous and coherent deployment of all the results offer the reader a comprehensive and sound understanding of the topic of locally convex quasi-*-algebras. The authors provide a clear view of the possible directions of future research in the field.” (Ioannis Zarakas, Mathematical Reviews, August, 2022)

“This book is well written and can be recommended both to experts on locally convex quasi *-algebras as well as to young researchers (not only in mathematics, but also in physics) who want to understand the ‘world of quasi *-algebras’ (in the general case or in the normed or locally convex setting).” (Mart Abel, zbMATH 1447.46001, 2020)

• Department of Mathematics, National and Kapodistrian University of Athens, Athens, Greece

  Maria Fragoulopoulou

• Matematica e Informatica, Università degli Studi di Palermo, Palermo, Italy

  Camillo Trapani

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