Commutation Properties of Hilbert Space Operators and Related Topics (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge)

Calvin R. Putnam

ISBN 10: 3642859402 / ISBN 13: 9783642859403

Published by Springer 2012-05-03, 2012

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Seller Inventory # 6666-IUK-9783642859403

Bibliographic Details

• Title: Commutation Properties of Hilbert Space Operators and Related Topics (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge)
• Publisher: Springer 2012-05-03
• Publication Date: 2012
• Language: English
• ISBN 10: 3642859402
• ISBN 13: 9783642859403
• Binding: Paperback
• Condition: New

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Synopsis

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 dis­ 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 commuta­ 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 applica­ tions of the results obtained are made to quantum mechanics, perturba­ tion theory, Laurent and Toeplitz operators, singular integral trans­ formations, and Jacobi matrices.