| Commutation Properties of Hilbert Space Operators and Related Topics Softcover Repri Edition Contributor(s): Putnam, Calvin R. (Author) |
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ISBN: 3642859402 ISBN-13: 9783642859403 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: May 2012 |
| Additional Information |
| BISAC Categories: - Mathematics | Functional Analysis - Mathematics | Calculus |
| Dewey: 515.724 |
| Series: Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge |
| Physical Information: 0.38" H x 6.14" W x 9.21" (0.57 lbs) 168 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |