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Commutation Properties of Hilbert Space Operators and Related Topics

  • Book
  • © 1967

Overview

Authors:
  1. C. R. Putnam

    1. Division of Mathematical Sciences, Purdue University, Lafayette, USA

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Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (MATHE2, volume 36)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-XI
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  2. Commutators of bounded operators

    • C. R. Putnam
    Pages 1-14

  3. Commutators and spectral theory

    • C. R. Putnam
    Pages 15-41

  4. Semi-normal operators

    • C. R. Putnam
    Pages 42-62

  5. Commutation relations in quantum mechanics

    • C. R. Putnam
    Pages 63-92

  6. Wave operators and unitary equivalence of self-adjoint operators

    • C. R. Putnam
    Pages 93-126

  7. Laurent and Toeplitz operators, singular integral operators and Jacobi matrices

    • C. R. Putnam
    Pages 127-146

  8. Back Matter

    Pages 147-167
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Keywords

About this book

What could be regarded as the beginning of a theory of commutators AB - BA of operators A and B on a Hilbert space, considered as a disยญ cipline in itself, goes back at least to the two papers of Weyl [3] {1928} and von Neumann [2] {1931} on quantum mechanics and the commutaยญ tion relations occurring there. Here A and B were unbounded self-adjoint operators satisfying the relation AB - BA = iI, in some appropriate sense, and the problem was that of establishing the essential uniqueness of the pair A and B. The study of commutators of bounded operators on a Hilbert space has a more recent origin, which can probably be pinpointed as the paper of Wintner [6] {1947}. An investigation of a few related topics in the subject is the main concern of this brief monograph. The ensuing work considers commuting or "almost" commuting quantities A and B, usually bounded or unbounded operators on a Hilbert space, but occasionally regarded as elements of some normed space. An attempt is made to stress the role of the commutator AB - BA, and to investigate its properties, as well as those of its components A and B when the latter are subject to various restrictions. Some applicaยญ tions of the results obtained are made to quantum mechanics, perturbaยญ tion theory, Laurent and Toeplitz operators, singular integral transยญ formations, and Jacobi matrices.

Authors and Affiliations

  • Division of Mathematical Sciences, Purdue University, Lafayette, USA

    C. R. Putnam

Bibliographic Information

  • Book Title: Commutation Properties of Hilbert Space Operators and Related Topics

  • Authors: C. R. Putnam

  • Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge

  • DOI: https://doi.org/10.1007/978-3-642-85938-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag, Berlin ยท Heidelberg 1967

  • Softcover ISBN: 978-3-642-85940-3Published: 03 May 2012

  • eBook ISBN: 978-3-642-85938-0Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XII, 168

  • Topics: Operator Theory

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