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Tomita-Takesaki Theory in Algebras of Unbounded Operators

  • Book
  • © 1998

Overview

Authors:
  1. Atsushi Inoue
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1699)

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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.

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-VII
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  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
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