Matrix Norms and their Applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1988
|
| Schriftenreihe: | Operator Theory: Advances and Applications
36 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | CHAPTER 1 - OPERATORS IN FINITE-DIMENSIONAL NORMED SPACES 1 §l. Norms of vectors, linear functionals, and linear operators. 1 § 2. Survey of spectral theory 14 § 3. Spectral radius . 17 § 4. One-parameter groups and semigroups of operators. 25 Appendix. Conditioning in general computational problems 28 CHAPTER 2 - SPECTRAL PROPERTIES OF CONTRACTIONS 33 §l. Contractive operators and isometries. 33 §2. Stability theorems. 46 §3. One-parameter semigroups of contractions and groups of isometries. 48 § 4. The boundary spectrum of extremal contractions. 52 §5. Extreme points of the unit ball in the space of operators. 64 §6. Critical exponents. 66 §7. The apparatus of functions on graphs. 72 §8. Combinatorial and spectral properties of t -contractions . 81 00 §9. Combinatorial and spectral properties of 96 nonnegative matrices. §10. Finite Markov chains. 102 §ll. Nonnegative projectors. 108 VI CHAPTER 3 - OPERATOR NORMS . 113 §l. Ring norms on the algebra of operators in E 113 §2. Characterization of operator norms. 126 §3. Operator minorants. . . . . . 133 §4. Suprema of families of operator norms 141 §5. Ring cross-norms . . 150 §6. Orthogonally-invariant norms. 152 CHAPTER 4 - STUDY OF THE ORDER STRUCTURE ON THE SET OF RING NORMS . 157 §l. Maximal chains of ring norms. 157 §2. Generalized ring norms. 160 §3. The lattice of subalgebras of the algebra End(E) 166 § 4 • Characterization of automorphisms 179 201 Brief Comments on the Literature 205 References . |
| Beschreibung: | 1 Online-Ressource (VIII, 210 p) |
| ISBN: | 9783034874007 9783764322205 |
| DOI: | 10.1007/978-3-0348-7400-7 |
Internformat
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Datensatz im Suchindex
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| author | Belitskii, G. R. |
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| dewey-full | 50 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 050 - General serial publications |
| dewey-raw | 50 |
| dewey-search | 50 |
| dewey-sort | 250 |
| dewey-tens | 050 - General serial publications |
| discipline | Allgemeine Naturwissenschaft Mathematik |
| doi_str_mv | 10.1007/978-3-0348-7400-7 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034874007 9783764322205 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857344 |
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| spelling | Belitskii, G. R. Verfasser aut Matrix Norms and their Applications by G. R. Belitskii, Yurii I. Lyubich Basel Birkhäuser Basel 1988 1 Online-Ressource (VIII, 210 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory: Advances and Applications 36 CHAPTER 1 - OPERATORS IN FINITE-DIMENSIONAL NORMED SPACES 1 §l. Norms of vectors, linear functionals, and linear operators. 1 § 2. Survey of spectral theory 14 § 3. Spectral radius . 17 § 4. One-parameter groups and semigroups of operators. 25 Appendix. Conditioning in general computational problems 28 CHAPTER 2 - SPECTRAL PROPERTIES OF CONTRACTIONS 33 §l. Contractive operators and isometries. 33 §2. Stability theorems. 46 §3. One-parameter semigroups of contractions and groups of isometries. 48 § 4. The boundary spectrum of extremal contractions. 52 §5. Extreme points of the unit ball in the space of operators. 64 §6. Critical exponents. 66 §7. The apparatus of functions on graphs. 72 §8. Combinatorial and spectral properties of t -contractions . 81 00 §9. Combinatorial and spectral properties of 96 nonnegative matrices. §10. Finite Markov chains. 102 §ll. Nonnegative projectors. 108 VI CHAPTER 3 - OPERATOR NORMS . 113 §l. Ring norms on the algebra of operators in E 113 §2. Characterization of operator norms. 126 §3. Operator minorants. . . . . . 133 §4. Suprema of families of operator norms 141 §5. Ring cross-norms . . 150 §6. Orthogonally-invariant norms. 152 CHAPTER 4 - STUDY OF THE ORDER STRUCTURE ON THE SET OF RING NORMS . 157 §l. Maximal chains of ring norms. 157 §2. Generalized ring norms. 160 §3. The lattice of subalgebras of the algebra End(E) 166 § 4 • Characterization of automorphisms 179 201 Brief Comments on the Literature 205 References . Science (General) Science, general Naturwissenschaft Matrixnorm (DE-588)4210047-1 gnd rswk-swf Matrixnorm (DE-588)4210047-1 s 1\p DE-604 Lyubich, Yurii I. Sonstige oth https://doi.org/10.1007/978-3-0348-7400-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Belitskii, G. R. Matrix Norms and their Applications Science (General) Science, general Naturwissenschaft Matrixnorm (DE-588)4210047-1 gnd |
| subject_GND | (DE-588)4210047-1 |
| title | Matrix Norms and their Applications |
| title_auth | Matrix Norms and their Applications |
| title_exact_search | Matrix Norms and their Applications |
| title_full | Matrix Norms and their Applications by G. R. Belitskii, Yurii I. Lyubich |
| title_fullStr | Matrix Norms and their Applications by G. R. Belitskii, Yurii I. Lyubich |
| title_full_unstemmed | Matrix Norms and their Applications by G. R. Belitskii, Yurii I. Lyubich |
| title_short | Matrix Norms and their Applications |
| title_sort | matrix norms and their applications |
| topic | Science (General) Science, general Naturwissenschaft Matrixnorm (DE-588)4210047-1 gnd |
| topic_facet | Science (General) Science, general Naturwissenschaft Matrixnorm |
| url | https://doi.org/10.1007/978-3-0348-7400-7 |
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