Advertisement

© 2020

Locally Convex Quasi *-Algebras and their Representations

Book
  • 1.3k Downloads

Part of the Lecture Notes in Mathematics book series (LNM, volume 2257)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Maria Fragoulopoulou, Camillo Trapani
    Pages 1-7
  3. Maria Fragoulopoulou, Camillo Trapani
    Pages 9-29
  4. Maria Fragoulopoulou, Camillo Trapani
    Pages 31-66
  5. Maria Fragoulopoulou, Camillo Trapani
    Pages 67-94
  6. Maria Fragoulopoulou, Camillo Trapani
    Pages 95-142
  7. Maria Fragoulopoulou, Camillo Trapani
    Pages 143-161
  8. Maria Fragoulopoulou, Camillo Trapani
    Pages 163-200
  9. Back Matter
    Pages 201-262

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  1. 1.Department of MathematicsNational and Kapodistrian University of AthensAthensGreece
  2. 2.Matematica e InformaticaUniversità degli Studi di PalermoPalermoItaly

Bibliographic information

Industry Sectors
Finance, Business & Banking

Reviews

“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)