Commutation Properties of Hilbert Space Operators and Related Topics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1967
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete
36 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 discipline in itself, goes back at least to the two papers of Weyl [3] {1928} and von Neumann [2] {1931} on quantum mechanics and the commutation 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 applications of the results obtained are made to quantum mechanics, perturbation theory, Laurent and Toeplitz operators, singular integral transformations, and Jacobi matrices |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9783642859380 9783642859403 |
| DOI: | 10.1007/978-3-642-85938-0 |
Internformat
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Datensatz im Suchindex
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| author | Putnam, C. R. |
| author_facet | Putnam, C. R. |
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| dewey-sort | 3510 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-85938-0 |
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| id | DE-604.BV042423056 |
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| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642859380 9783642859403 |
| language | English |
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| publishDate | 1967 |
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| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spelling | Putnam, C. R. Verfasser aut Commutation Properties of Hilbert Space Operators and Related Topics by C. R. Putnam Berlin, Heidelberg Springer Berlin Heidelberg 1967 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 36 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 discipline in itself, goes back at least to the two papers of Weyl [3] {1928} and von Neumann [2] {1931} on quantum mechanics and the commutation 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 applications of the results obtained are made to quantum mechanics, perturbation theory, Laurent and Toeplitz operators, singular integral transformations, and Jacobi matrices Mathematics Mathematics, general Mathematik Vertauschbarer Operator (DE-588)4192247-5 gnd rswk-swf Kommutator Algebra (DE-588)4164826-2 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Operator (DE-588)4130529-2 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 s Kommutator Algebra (DE-588)4164826-2 s 1\p DE-604 Vertauschbarer Operator (DE-588)4192247-5 s 2\p DE-604 Operator (DE-588)4130529-2 s 3\p DE-604 Ergebnisse der Mathematik und ihrer Grenzgebiete 36 (DE-604)BV020546983 36 https://doi.org/10.1007/978-3-642-85938-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Putnam, C. R. Commutation Properties of Hilbert Space Operators and Related Topics Ergebnisse der Mathematik und ihrer Grenzgebiete Mathematics Mathematics, general Mathematik Vertauschbarer Operator (DE-588)4192247-5 gnd Kommutator Algebra (DE-588)4164826-2 gnd Hilbert-Raum (DE-588)4159850-7 gnd Operator (DE-588)4130529-2 gnd |
| subject_GND | (DE-588)4192247-5 (DE-588)4164826-2 (DE-588)4159850-7 (DE-588)4130529-2 |
| title | Commutation Properties of Hilbert Space Operators and Related Topics |
| title_auth | Commutation Properties of Hilbert Space Operators and Related Topics |
| title_exact_search | Commutation Properties of Hilbert Space Operators and Related Topics |
| title_full | Commutation Properties of Hilbert Space Operators and Related Topics by C. R. Putnam |
| title_fullStr | Commutation Properties of Hilbert Space Operators and Related Topics by C. R. Putnam |
| title_full_unstemmed | Commutation Properties of Hilbert Space Operators and Related Topics by C. R. Putnam |
| title_short | Commutation Properties of Hilbert Space Operators and Related Topics |
| title_sort | commutation properties of hilbert space operators and related topics |
| topic | Mathematics Mathematics, general Mathematik Vertauschbarer Operator (DE-588)4192247-5 gnd Kommutator Algebra (DE-588)4164826-2 gnd Hilbert-Raum (DE-588)4159850-7 gnd Operator (DE-588)4130529-2 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Vertauschbarer Operator Kommutator Algebra Hilbert-Raum Operator |
| url | https://doi.org/10.1007/978-3-642-85938-0 |
| volume_link | (DE-604)BV020546983 |
| work_keys_str_mv | AT putnamcr commutationpropertiesofhilbertspaceoperatorsandrelatedtopics |