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Uniqueness of the Injective III1 Factor

  • Book
  • © 1989

Overview

Authors:
  1. Steve Wright
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1413)

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About this book

Based on lectures delivered to the Seminar on Operator Algebras at Oakland University during the Winter semesters of 1985 and 1986, these notes are a detailed exposition of recent work of A. Connes and U. Haagerup which together constitute a proof that all injective factors of type III1 which act on a separable Hilbert space are isomorphic. This result disposes of the final open case in the classification of the separably acting injective factors, and is one of the outstanding recent achievements in the theory of operator algebras. The notes will be of considerable interest to specialists in operator algebras, operator theory and workers in allied areas such as quantum statistical mechanics and the theory of group representations.

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Table of contents (3 chapters)

  1. Front Matter

    Pages I-III
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  2. Introduction

    • Steve Wright
    Pages 1-8

  3. Connes' reduction of the uniqueness proof to the bicentralizer problem

    • Steve Wright
    Pages 9-81

  4. Haagerup's solution of the bicentralizer problem

    • Steve Wright
    Pages 82-105

  5. Back Matter

    Pages 106-108
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Bibliographic Information

  • Book Title: Uniqueness of the Injective III1 Factor

  • Authors: Steve Wright

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0090178

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1989

  • Softcover ISBN: 978-3-540-52130-3Published: 13 December 1989

  • eBook ISBN: 978-3-540-46903-2Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VI, 114

  • Topics: Analysis, Theoretical, Mathematical and Computational Physics

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