Lie algebras of bounded operators:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2001
|
| Series: | Operator theory
120 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 217 S. |
| ISBN: | 3764364041 |
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| 100 | 1 | |a Beltiţă, Daniel |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Lie algebras of bounded operators |c Daniel Beltiţă ; Mihai Şabac |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2001 | |
| 300 | |a VIII, 217 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 7 | |a ÁLGEBRAS DE LIE |2 larpcal | |
| 650 | 4 | |a Lie algebras | |
| 650 | 4 | |a Operator theory | |
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Record in the Search Index
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| adam_text | Contents
Introduction vii
I Preliminaries
A Lie Algebras
§ 1 Basic facts 1
§ 2 Ideals, solvability, nilpotence, radical and semisimplicity 4
§ 3 Sp classes of solvable Lie algebras 8
§ 4 Radical splitting theorems 10
§ 5 Cartan subalgebras 11
§ 6 The Killing form and compact Lie algebras 15
§ 7 Lie * algebras 16
B Complexes
§8 Generalities 23
§ 9 Banach space complexes 31
§ 10 Koszul complexes 33
§ 11 Operations with the Koszul complexes:
duality and tensor products 52
C Spectral Theory in Complex Banach Space
§ 12 General spectral theory and
decomposable operators 63
§ 13 The transformation of the spectral maximal
subspaces by bounded operators 68
§ 14 Special classes of decomposable operators 71
Notes 77
II The Commutators and Nilpotence Criteria
§ 15 An asymptotic formula for the commutators 81
§ 16 Nilpotence criteria in an associative algebra 89
§ 17 Quasinilpotence and nilpotence criteria
in complex Banach algebras 91
§ 18 Nilpotent elements in LM decomposable
Lie subalgebras of an associative algebra 95
vi Contents
§ 19 Nilpotent elements in LM decomposable
Lie algebras of bounded linear operators 101
Notes 101
III Infinite dimensional Variants of the Lie and Engel Theorems
§ 20 Weights for operator algebras 103
§ 21 Invariant subspaces for LM decomposable
Lie algebras of bounded operators 114
§ 22 The irreducible representations of an
LM decomposable Lie algebra.
Infinite dimensional variant of Lie s Theorem
on a complex Banach space 121
§ 23 The associative envelope of a
Lie algebra of quasinilpotent operators 126
§ 24 Commutativity modulo the Jacobson radical 129
Notes 131
IV Spectral Theory for Solvable Lie Algebras of Operators
§ 25 Spectral theory for representations of Lie algebras 133
§ 26 Spectral theory for systems of operators
generating nilpotent Lie algebras 150
§ 27 The Cartan Taylor spectrum of
a locally solvable Lie algebra of operators 163
§28 Lie ideals of generalized spectral operators 173
Notes 180
V Semisimple Lie Algebras of Operators
§ 29 Lie subalgebra with involution consisting
of bounded operators on a complex Banach space.
Normal elements given by a space of
self adjoint operators 181
§ 30 Individual spectral properties in ideally finite
semisimple Lie algebras of operators 188
§ 31 Semisimple Lie algebras of compact
quasinilpotent operators 198
Notes 202
Bibliography 203
Index 215
List of Symbols 219
|
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| id | DE-604.BV013325287 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:43:51Z |
| institution | BVB |
| isbn | 3764364041 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009087592 |
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| physical | VIII, 217 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Beltiţă, Daniel Verfasser aut Lie algebras of bounded operators Daniel Beltiţă ; Mihai Şabac Basel [u.a.] Birkhäuser 2001 VIII, 217 S. txt rdacontent n rdamedia nc rdacarrier Operator theory 120 OPERADORES (ANÁLISE FUNCIONAL) (TEORIA) larpcal ÁLGEBRAS DE LIE larpcal Lie algebras Operator theory 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 DE-604 Şabac, Mihai Verfasser aut Operator theory 120 (DE-604)BV000000970 120 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009087592&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beltiţă, Daniel Şabac, Mihai Lie algebras of bounded operators Operator theory OPERADORES (ANÁLISE FUNCIONAL) (TEORIA) larpcal ÁLGEBRAS DE LIE larpcal Lie algebras Operator theory 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 Daniel Beltiţă ; Mihai Şabac |
| title_fullStr | Lie algebras of bounded operators Daniel Beltiţă ; Mihai Şabac |
| title_full_unstemmed | Lie algebras of bounded operators Daniel Beltiţă ; Mihai Şabac |
| title_short | Lie algebras of bounded operators |
| title_sort | lie algebras of bounded operators |
| topic | OPERADORES (ANÁLISE FUNCIONAL) (TEORIA) larpcal ÁLGEBRAS DE LIE larpcal Lie algebras Operator theory Beschränkter Operator (DE-588)4233452-4 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | OPERADORES (ANÁLISE FUNCIONAL) (TEORIA) ÁLGEBRAS DE LIE Lie algebras Operator theory Beschränkter Operator Lie-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009087592&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
| work_keys_str_mv | AT beltitadaniel liealgebrasofboundedoperators AT sabacmihai liealgebrasofboundedoperators |