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Partial *-Algebras and Their Operator Realizations

  • Jean-Pierre Antoine
  • Atsushi Inoue
  • Camillo Trapani

Part of the Mathematics and Its Applications book series (MAIA, volume 553)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Theory of Partial O*-Algebras

    1. Front Matter
      Pages 1-1
    2. Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 3-42
    3. Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 43-95
    4. Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 97-127
    5. Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 129-163
    6. Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 165-253
  3. Theory of Partial *-Algebras

    1. Front Matter
      Pages 255-255
    2. Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 257-300
    3. Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 301-337
    4. Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 339-365
    5. Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 367-427
    6. Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 429-468
    7. Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 469-492
    8. Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 493-494
  4. Back Matter
    Pages 495-521

About this book

Introduction

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*-algebras, basic properties, examples, topologies on them. The climax is the generalization to this new framework of the celebrated modular theory of Tomita-Takesaki, one of the cornerstones for the applications to statistical physics.
The second part focuses on abstract partial *-algebras and their representation theory, obtaining again generalizations of familiar theorems (Radon-Nikodym, Lebesgue).

Keywords

C*-algebra Hilbert space Topology algebra theorem

Authors and affiliations

  • Jean-Pierre Antoine
    • 1
  • Atsushi Inoue
    • 2
  • Camillo Trapani
    • 3
  1. 1.Institut de Physique ThéoriqueUniversité Catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Department of Applied MathematicsFukuoka UniversityFukuokaJapan
  3. 3.Dipartimento di Matematica ed ApplicazioniUniversità di PalermoPalermoItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-0065-8
  • Copyright Information Springer Science+Business Media B.V. 2002
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6176-8
  • Online ISBN 978-94-017-0065-8
  • Buy this book on publisher's site
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