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Unbounded Non-Commutative Integration

  • Book
  • © 1985

Overview

Authors:
  1. J. P. Jurzak

    1. Physique-Mathématique, Université de Dijon, France

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Part of the book series: Mathematical Physics Studies (MPST, volume 7)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xx
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  2. Examples and Observations

    • J. P. Jurzak
    Pages 1-6

  3. Main Spaces

    • J. P. Jurzak
    Pages 7-20

  4. Density Theorems

    • J. P. Jurzak
    Pages 21-29

  5. Technical Properties of the Domain

    • J. P. Jurzak
    Pages 30-56

  6. Elementary Operations

    • J. P. Jurzak
    Pages 57-64

  7. Gelfand Transformation

    • J. P. Jurzak
    Pages 65-82

  8. Cofinal Central Systems and Derivations

    • J. P. Jurzak
    Pages 83-98

  9. Notion of Representation: The G.N.S. Case

    • J. P. Jurzak
    Pages 99-132

  10. The State Space

    • J. P. Jurzak
    Pages 133-153

  11. G-Invariance and G-Traces

    • J. P. Jurzak
    Pages 154-168

  12. Other Commutation Theorems

    • J. P. Jurzak
    Pages 169-178

  13. On Strong and Ultrastrong Topologies

    • J. P. Jurzak
    Pages 179-188

  14. Back Matter

    Pages 189-191
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Keywords

About this book

Non-commutative integration has its origin in the classical papers of Murray and von Neumann on rings of operators, and was introduced because of unsolved problems in unitary group representations and the elucidation of various aspects of quantum-mechanical formalism, together with formal calculus in such operator rings. These papers emphasized the interest in 1I -factors and pOinted out the remarkable behavior and 1 algebraic structure of the set of all unbounded closed operators a. ffiliated to such rings. The absence of power tools in functional analysis - mainly settled in their definitive form by A. Grothendieck around 1950-195- together with the pathological manipulation of algebraic operations on closed operators in Hilbert spaces, has limited ring-theory to the study of algebras of bounded operators with the main objective the difficult question of classifica­ tion up to isomorphisms of factors. This material has permitted a rigorous study of discrete systems in statistical mechanics but appears to be less convincing in other domains of physics (in the algebraic approach to field theory, for example). The striking role of Hamiltonians, Schrodinger operators and Lie group invariant properties in such areas of physics disappears in the so­ called C*-approach.

Authors and Affiliations

  • Physique-Mathématique, Université de Dijon, France

    J. P. Jurzak

Bibliographic Information

  • Book Title: Unbounded Non-Commutative Integration

  • Authors: J. P. Jurzak

  • Series Title: Mathematical Physics Studies

  • DOI: https://doi.org/10.1007/978-94-009-5231-7

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: D. Reidel Publishing Company, Dordretch, Holland 1985

  • Hardcover ISBN: 978-90-277-1815-0Published: 30 June 1985

  • Softcover ISBN: 978-94-010-8813-8Published: 19 October 2011

  • eBook ISBN: 978-94-009-5231-7Published: 06 December 2012

  • Series ISSN: 0921-3767

  • Series E-ISSN: 2352-3905

  • Edition Number: 1

  • Number of Pages: XX, 191

  • Topics: Theoretical, Mathematical and Computational Physics

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