Lie Algebras of Bounded Operators:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2001
|
| Schriftenreihe: | Operator Theory: Advances and Applications
120 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In several proofs from the theory of finite-dimensional Lie algebras, an essential contribution comes from the Jordan canonical structure of linear maps acting on finite-dimensional vector spaces. On the other hand, there exist classical results concerning Lie algebras which advise us to use infinite-dimensional vector spaces as well. For example, the classical Lie Theorem asserts that all finite-dimensional irreducible representations of solvable Lie algebras are one-dimensional. Hence, from this point of view, the solvable Lie algebras cannot be distinguished from one another, that is, they cannot be classified. Even this example alone urges the infinite-dimensional vector spaces to appear on the stage. But the structure of linear maps on such a space is too little understood; for these linear maps one cannot speak about something like the Jordan canonical structure of matrices. Fortunately there exists a large class of linear maps on vector spaces of arbi trary dimension, having some common features with the matrices. We mean the bounded linear operators on a complex Banach space. Certain types of bounded operators (such as the Dunford spectral, Foia§ decomposable, scalar generalized or Colojoara spectral generalized operators) actually even enjoy a kind of Jordan decomposition theorem. One of the aims of the present book is to expound the most important results obtained until now by using bounded operators in the study of Lie algebras |
| Beschreibung: | 1 Online-Ressource (VIII, 219 p) |
| ISBN: | 9783034883320 9783034895200 |
| DOI: | 10.1007/978-3-0348-8332-0 |
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| 500 | |a In several proofs from the theory of finite-dimensional Lie algebras, an essential contribution comes from the Jordan canonical structure of linear maps acting on finite-dimensional vector spaces. On the other hand, there exist classical results concerning Lie algebras which advise us to use infinite-dimensional vector spaces as well. For example, the classical Lie Theorem asserts that all finite-dimensional irreducible representations of solvable Lie algebras are one-dimensional. Hence, from this point of view, the solvable Lie algebras cannot be distinguished from one another, that is, they cannot be classified. Even this example alone urges the infinite-dimensional vector spaces to appear on the stage. But the structure of linear maps on such a space is too little understood; for these linear maps one cannot speak about something like the Jordan canonical structure of matrices. Fortunately there exists a large class of linear maps on vector spaces of arbi trary dimension, having some common features with the matrices. We mean the bounded linear operators on a complex Banach space. Certain types of bounded operators (such as the Dunford spectral, Foia§ decomposable, scalar generalized or Colojoara spectral generalized operators) actually even enjoy a kind of Jordan decomposition theorem. One of the aims of the present book is to expound the most important results obtained until now by using bounded operators in the study of Lie algebras | ||
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8332-0 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034883320 9783034895200 |
| language | English |
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| physical | 1 Online-Ressource (VIII, 219 p) |
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| spelling | Beltiţă, Daniel Verfasser aut Lie Algebras of Bounded Operators by Daniel Beltiţă, Mihai Şabac Basel Birkhäuser Basel 2001 1 Online-Ressource (VIII, 219 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory: Advances and Applications 120 In several proofs from the theory of finite-dimensional Lie algebras, an essential contribution comes from the Jordan canonical structure of linear maps acting on finite-dimensional vector spaces. On the other hand, there exist classical results concerning Lie algebras which advise us to use infinite-dimensional vector spaces as well. For example, the classical Lie Theorem asserts that all finite-dimensional irreducible representations of solvable Lie algebras are one-dimensional. Hence, from this point of view, the solvable Lie algebras cannot be distinguished from one another, that is, they cannot be classified. Even this example alone urges the infinite-dimensional vector spaces to appear on the stage. But the structure of linear maps on such a space is too little understood; for these linear maps one cannot speak about something like the Jordan canonical structure of matrices. Fortunately there exists a large class of linear maps on vector spaces of arbi trary dimension, having some common features with the matrices. We mean the bounded linear operators on a complex Banach space. Certain types of bounded operators (such as the Dunford spectral, Foia§ decomposable, scalar generalized or Colojoara spectral generalized operators) actually even enjoy a kind of Jordan decomposition theorem. One of the aims of the present book is to expound the most important results obtained until now by using bounded operators in the study of Lie algebras Mathematics Mathematics, general Mathematik Beschränkter Operator (DE-588)4233452-4 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s Beschränkter Operator (DE-588)4233452-4 s 1\p DE-604 Şabac, Mihai Sonstige oth https://doi.org/10.1007/978-3-0348-8332-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Beltiţă, Daniel Lie Algebras of Bounded Operators Mathematics Mathematics, general Mathematik Beschränkter Operator (DE-588)4233452-4 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4233452-4 (DE-588)4130355-6 |
| title | Lie Algebras of Bounded Operators |
| title_auth | Lie Algebras of Bounded Operators |
| title_exact_search | Lie Algebras of Bounded Operators |
| title_full | Lie Algebras of Bounded Operators by Daniel Beltiţă, Mihai Şabac |
| title_fullStr | Lie Algebras of Bounded Operators by Daniel Beltiţă, Mihai Şabac |
| title_full_unstemmed | Lie Algebras of Bounded Operators by Daniel Beltiţă, Mihai Şabac |
| title_short | Lie Algebras of Bounded Operators |
| title_sort | lie algebras of bounded operators |
| topic | Mathematics Mathematics, general Mathematik Beschränkter Operator (DE-588)4233452-4 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Beschränkter Operator Lie-Algebra |
| url | https://doi.org/10.1007/978-3-0348-8332-0 |
| work_keys_str_mv | AT beltitadaniel liealgebrasofboundedoperators AT sabacmihai liealgebrasofboundedoperators |