Tomita-Takesaki Theory in Algebras of Unbounded Operators

  • Authors
  • Atsushi┬áInoue

Part of the Lecture Notes in Mathematics book series (LNM, volume 1699)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Atsushi Inoue
    Pages 1-5
  3. Atsushi Inoue
    Pages 7-40
  4. Atsushi Inoue
    Pages 41-110
  5. Atsushi Inoue
    Pages 111-168
  6. Atsushi Inoue
    Pages 169-223
  7. Back Matter
    Pages 225-243

About this book

Introduction

These notes are devoted to a systematic study of developing the Tomita-Takesaki theory for von Neumann algebras in unbounded operator algebras called O*-algebras and to its applications to quantum physics. The notions of standard generalized vectors and standard weights for an O*-algebra are introduced and they lead to a Tomita-Takesaki theory of modular automorphisms. The Tomita-Takesaki theory in O*-algebras is applied to quantum moment problem, quantum statistical mechanics and the Wightman quantum field theory. This will be of interest to graduate students and researchers in the field of (unbounded) operator algebras and mathematical physics.

Keywords

Algebra O*-algebras Tomita-Takesaki theory generalized von Neumann algebras mathematical physics modular generalized vectors standard generalized vectors standard weights

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0093329
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-65194-9
  • Online ISBN 978-3-540-49495-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book