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Partial *- Algebras and Their Operator Realizations

  • Book
  • © 2002

Overview

Authors:
  1. Jean-Pierre Antoine

    1. Institut de Physique Théorique, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

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  2. Atsushi Inoue

    1. Department of Applied Mathematics, Fukuoka University, Fukuoka, Japan

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  3. Camillo Trapani

    1. Dipartimento di Matematica ed Applicazioni, Università di Palermo, Palermo, Italy

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

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Table of contents (12 chapters)

  1. Front Matter

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

    1. Front Matter

      Pages 1-1
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    2. Unbounded Linear Operators in Hilbert Spaces

      • Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 3-42

    3. Partial O*-Algebras

      • Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 43-95

    4. Commutative Partial O*-Algebras

      • Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 97-127

    5. Topologies on Partial O*-Algebras

      • Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 129-163

    6. Tomita—Takesaki Theory in Partial O*-Algebras

      • Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 165-253

  3. Theory of Partial *-Algebras

    1. Front Matter

      Pages 255-255
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    2. Partial *-Algebras

      • Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 257-300

    3. *-Representations of Partial *-Algebras

      • Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 301-337

    4. Well-behaved *-Representations

      • Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 339-365

    5. Biweights on Partial *-Algebras

      • Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 367-427

    6. Quasi *-Algebras of Operators in Rigged Hilbert Spaces

      • Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 429-468

    7. Physical Applications

      • Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 469-492

    8. Outcome

      • Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani
      Pages 493-494

  4. Back Matter

    Pages 495-521
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Keywords

About this book

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).

Authors and Affiliations

  • Institut de Physique Théorique, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Jean-Pierre Antoine

  • Department of Applied Mathematics, Fukuoka University, Fukuoka, Japan

    Atsushi Inoue

  • Dipartimento di Matematica ed Applicazioni, Università di Palermo, Palermo, Italy

    Camillo Trapani

Bibliographic Information

  • Book Title: Partial *- Algebras and Their Operator Realizations

  • Authors: Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani

  • Series Title: Mathematics and Its Applications

  • DOI: https://doi.org/10.1007/978-94-017-0065-8

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2002

  • Hardcover ISBN: 978-1-4020-1025-5Published: 31 December 2002

  • Softcover ISBN: 978-90-481-6176-8Published: 04 December 2010

  • eBook ISBN: 978-94-017-0065-8Published: 29 June 2013

  • Edition Number: 1

  • Number of Pages: XX, 522

  • Topics: Analysis, Operator Theory, Mathematics, general

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