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  • © 1998

Tomita-Takesaki Theory in Algebras of Unbounded Operators

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-VII
  2. Introduction

    • Atsushi Inoue
    Pages 1-5
  3. Fundamentals of O*-algebras

    • Atsushi Inoue
    Pages 7-40
  4. Standard systems and modular systems

    • Atsushi Inoue
    Pages 41-110
  5. Standard weights on O*-algebras

    • Atsushi Inoue
    Pages 111-168
  6. Physical applications

    • Atsushi Inoue
    Pages 169-223
  7. Back Matter

    Pages 225-243

About this book

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

  • Book Title: Tomita-Takesaki Theory in Algebras of Unbounded Operators

  • Authors: Atsushi Inoue

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0093329

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • Softcover ISBN: 978-3-540-65194-9Published: 18 November 1998

  • eBook ISBN: 978-3-540-49495-9Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 244

  • Topics: Algebra, Operator Theory, Quantum Physics, Spintronics

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions