Unbounded Operator Algebras and Representation Theory:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1990
|
| Schriftenreihe: | Operator Theory: Advances and Applications
37 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-3-0348-7469-4 |
| Beschreibung: | *-algebras of unbounded operators in Hilbert space, or more generally algebraic systems of unbounded operators, occur in a natural way in unitary representation theory of Lie groups and in the Wightman formulation of quantum field theory. In representation theory they appear as the images of the associated representations of the Lie algebras or of the enveloping algebras on the Garding domain and in quantum field theory they occur as the vector space of field operators or the *-algebra generated by them. Some of the basic tools for the general theory were first introduced and used in these fields. For instance, the notion of the weak (bounded) commutant which plays a fundamental role in thegeneraltheory had already appeared in quantum field theory early in the sixties. Nevertheless, a systematic study of unbounded operator algebras began only at the beginning of the seventies. It was initiated by (in alphabetic order) BORCHERS, LASSNER, POWERS, UHLMANN and VASILIEV. From the very beginning, and still today, representation theory of Lie groups and Lie algebras and quantum field theory have been primary sources of motivation and also of examples. However, the general theory of unbounded operator algebras has also had points of contact with several other disciplines. In particular, the theory of locally convex spaces, the theory of von Neumann algebras, distribution theory, single operator theory, the moment problem and its non-commutative generalizations and noncommutative probability theory, all have interacted with our subject |
| Umfang: | 1 Online-Ressource (380 p) |
| ISBN: | 9783034874694 9783034874717 |
| DOI: | 10.1007/978-3-0348-7469-4 |
Internformat
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| 500 | |a *-algebras of unbounded operators in Hilbert space, or more generally algebraic systems of unbounded operators, occur in a natural way in unitary representation theory of Lie groups and in the Wightman formulation of quantum field theory. In representation theory they appear as the images of the associated representations of the Lie algebras or of the enveloping algebras on the Garding domain and in quantum field theory they occur as the vector space of field operators or the *-algebra generated by them. Some of the basic tools for the general theory were first introduced and used in these fields. For instance, the notion of the weak (bounded) commutant which plays a fundamental role in thegeneraltheory had already appeared in quantum field theory early in the sixties. Nevertheless, a systematic study of unbounded operator algebras began only at the beginning of the seventies. It was initiated by (in alphabetic order) BORCHERS, LASSNER, POWERS, UHLMANN and VASILIEV. From the very beginning, and still today, representation theory of Lie groups and Lie algebras and quantum field theory have been primary sources of motivation and also of examples. However, the general theory of unbounded operator algebras has also had points of contact with several other disciplines. In particular, the theory of locally convex spaces, the theory of von Neumann algebras, distribution theory, single operator theory, the moment problem and its non-commutative generalizations and noncommutative probability theory, all have interacted with our subject | ||
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Datensatz im Suchindex
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| id | DE-604.BV042421932 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:45Z |
| institution | BVB |
| isbn | 9783034874694 9783034874717 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857349 |
| oclc_num | 879623124 |
| open_access_boolean | |
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| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (380 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Birkhäuser Basel |
| record_format | marc |
| series2 | Operator Theory: Advances and Applications |
| spellingShingle | Schmüdgen, Konrad 1947- Unbounded Operator Algebras and Representation Theory Mathematics Algebra Mathematik Unbeschränkter Operator (DE-588)4236037-7 gnd Operatoralgebra (DE-588)4129366-6 gnd Hilbert-Raum (DE-588)4159850-7 gnd Algebra mit Involution (DE-588)4236038-9 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4236037-7 (DE-588)4129366-6 (DE-588)4159850-7 (DE-588)4236038-9 (DE-588)4148816-7 |
| title | Unbounded Operator Algebras and Representation Theory |
| title_auth | Unbounded Operator Algebras and Representation Theory |
| title_exact_search | Unbounded Operator Algebras and Representation Theory |
| title_full | Unbounded Operator Algebras and Representation Theory by Konrad Schmüdgen |
| title_fullStr | Unbounded Operator Algebras and Representation Theory by Konrad Schmüdgen |
| title_full_unstemmed | Unbounded Operator Algebras and Representation Theory by Konrad Schmüdgen |
| title_short | Unbounded Operator Algebras and Representation Theory |
| title_sort | unbounded operator algebras and representation theory |
| topic | Mathematics Algebra Mathematik Unbeschränkter Operator (DE-588)4236037-7 gnd Operatoralgebra (DE-588)4129366-6 gnd Hilbert-Raum (DE-588)4159850-7 gnd Algebra mit Involution (DE-588)4236038-9 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | Mathematics Algebra Mathematik Unbeschränkter Operator Operatoralgebra Hilbert-Raum Algebra mit Involution Darstellungstheorie |
| url | https://doi.org/10.1007/978-3-0348-7469-4 |
| volume_link | (DE-604)BV035421307 |
| work_keys_str_mv | AT schmudgenkonrad unboundedoperatoralgebrasandrepresentationtheory |