Simultaneous triangularization:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2000
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 318 S. |
| ISBN: | 0387984674 0387984666 |
Staff View
MARC
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Record in the Search Index
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| adam_text | CONTENTS
Preface vii
Chapter One: Algebras of Matrices 1
1.1 The Triangularization Lemma 1
1.2 Burnside s Theorem 4
1.3 Triangularizability of Algebras of Matrices 6
1.4 Triangularization and the Radical 10
1.5 Block Triangularization and Characterizations
of Triangularizability 12
1.6 Approximate Commutativity 17
1.7 Nonassociative Algebras 21
1.8 Notes and Remarks 25
Chapter Two: Semigroups of Matrices 27
2.1 Basic Definitions and Propositions 27
2.2 Permutable Trace 33
2.3 Zero One Spectra 36
2.4 Notes and Remarks 41
Chapter Three: Spectral Conditions on Semigroups 43
3.1 Reduction to the Field of Complex Numbers 43
3.2 Permutable Spectrum 51
3.3 Submultiplicative Spectrum 55
3.4 Conditions on Spectral Radius 62
3.5 The Dominance Condition on Spectra 70
3.6 Notes and Remarks 73
Chapter Four: Finiteness Lemmas and
Further Spectral Conditions 75
4.1 Reductions to Finite Semigroups 75
4.2 Subadditive and Sublinear Spectra 80
4.3 Further Multiplicative Conditions on Spectra 89
4.4 Polynomial Conditions on Spectra 93
4.5 Notes and Remarks 102
Chapter Five: Semigroups of Nonnegative Matrices 104
5.1 Decomposability 104
5.2 Indecomposable Semigroups 115
5.3 Connections with Reducibility 127
5.4 Notes and Remarks 129
Chapter Six: Compact Operators and
Invariant Subspaces 130
6.1 Operators on Banach Spaces 130
xii Contents
6.2 Compact Operators 133
6.3 Invariant Subspaces for Compact Operators 135
6.4 The Riesz Decomposition of Compact Operators 138
6.5 Trace Class Operators on Hilbert Space 142
6.6 Notes and Remarks 149
Chapter Seven: Algebras of Compact Operators 151
7.1 The Definition of Triangularizability 151
7.2 Spectra from Triangular Forms 155
7.3 Lomonosov s Lemma and McCoy s Theorem 162
7.4 Transitive Algebras 167
7.5 Block Triangularization and Applications 173
7.6 Approximate Commutativity 183
7.7 Notes and Remarks 189
Chapter Eight: Semigroups of Compact Operators 193
8.1 Quasinilpotent Compact Operators 193
8.2 A General Approach 199
8.3 Permutability and Submultiplicativity of Spectra 205
8.4 Subadditivity and Sublinearity of Spectra 209
8.5 Polynomial Conditions on Spectra 213
8.6 Conditions on Spectral Radius and Trace 216
8.7 Nonnegative Operators 223
8.8 Notes and Remarks 241
Chapter Nine: Bounded Operators 244
9.1 Collections of Nilpotent Operators 244
9.2 Commutators of Rank One 250
9.3 Bands 262
9.4 Nonnegative Operators 272
9.5 Notes and Remarks 281
References 284
Notation Index 307
Author Index 309
Subject Index 315
|
| any_adam_object | 1 |
| author | Radjavi, Heydar Rosenthal, Peter |
| author_facet | Radjavi, Heydar Rosenthal, Peter |
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| classification_tum | MAT 540f |
| ctrlnum | (OCoLC)890153799 (DE-599)BVBBV012978827 |
| dewey-full | 512.9434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9434 |
| dewey-search | 512.9434 |
| dewey-sort | 3512.9434 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012978827 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:37:08Z |
| institution | BVB |
| isbn | 0387984674 0387984666 |
| language | English |
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| physical | XII, 318 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Radjavi, Heydar Verfasser aut Simultaneous triangularization Heydar Radjavi ; Peter Rosenthal New York [u.a.] Springer 2000 XII, 318 S. txt rdacontent n rdamedia nc rdacarrier Universitext Dreieckszerlegung - Lineare Transformation Triangularization (Mathematics) Matrizenalgebra (DE-588)4139347-8 gnd rswk-swf Triangulation (DE-588)4186017-2 gnd rswk-swf Dreieckszerlegung (DE-588)4324733-7 gnd rswk-swf Triangulation (DE-588)4186017-2 s DE-604 Matrizenalgebra (DE-588)4139347-8 s Dreieckszerlegung (DE-588)4324733-7 s Rosenthal, Peter Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008842734&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Radjavi, Heydar Rosenthal, Peter Simultaneous triangularization Dreieckszerlegung - Lineare Transformation Triangularization (Mathematics) Matrizenalgebra (DE-588)4139347-8 gnd Triangulation (DE-588)4186017-2 gnd Dreieckszerlegung (DE-588)4324733-7 gnd |
| subject_GND | (DE-588)4139347-8 (DE-588)4186017-2 (DE-588)4324733-7 |
| title | Simultaneous triangularization |
| title_auth | Simultaneous triangularization |
| title_exact_search | Simultaneous triangularization |
| title_full | Simultaneous triangularization Heydar Radjavi ; Peter Rosenthal |
| title_fullStr | Simultaneous triangularization Heydar Radjavi ; Peter Rosenthal |
| title_full_unstemmed | Simultaneous triangularization Heydar Radjavi ; Peter Rosenthal |
| title_short | Simultaneous triangularization |
| title_sort | simultaneous triangularization |
| topic | Dreieckszerlegung - Lineare Transformation Triangularization (Mathematics) Matrizenalgebra (DE-588)4139347-8 gnd Triangulation (DE-588)4186017-2 gnd Dreieckszerlegung (DE-588)4324733-7 gnd |
| topic_facet | Dreieckszerlegung - Lineare Transformation Triangularization (Mathematics) Matrizenalgebra Triangulation Dreieckszerlegung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008842734&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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