Matrix Norms and their Applications

Libuich

ISBN 10: 3764322209 / ISBN 13: 9783764322205

Editore: Birkhäuser Basel, Birkhäuser Basel Sep 1988, 1988

Riguardo questo articolo

This item is printed on demand - Print on Demand Titel. Neuware -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 . .Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 220 pp. Englisch.

Codice articolo 9783764322205

Dati bibliografici

• Titolo: Matrix Norms and their Applications
• Editore: Birkhäuser Basel, Birkhäuser Basel Sep 1988
• Data di pubblicazione: 1988
• Lingua: Inglese
• ISBN 10: 3764322209
• ISBN 13: 9783764322205
• Rilegatura: Taschenbuch
• Condizione: Neu

Descrizione articolo

Riassunto

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 . .

Contenuti

1 — Operators in Finite-Dimensional Normed Spaces.- §1. Norms of vectors, linear functionals, and linear operators.- §2. Survey of spectral theory.- §3. Spectral radius.- §4. One-parameter groups and semigroups of operators.- Appendix. Conditioning in general computational problems.- 2 — Spectral Properties of Contractions.- §1. Contractive operators and isometries.- §2. Stability theorems.- §3. One-parameter semigroups of contractions and groups of isometries.- §4. The boundary spectrum of extremal contractions.- §5. Extreme points of the unit ball in the space of operators.- §6. Critical exponents.- §7. The apparatus of functions on graphs.- §8. Combinatorial and spectral properties of l?-contractions.- §9. Combinatorial and spectral properties of nonnegative matrices.- §10. Finite Markov chains.- §11. Nonnegative projectors.- 3 — Operator Norms.- §1. Ring norms on the algebra of operators in E.- §2. Characterization of operator norms.- §3. Operator minorants.- §4. Suprema of families of operator norms.- §5. Ring cross-norms.- §6. Orthogonally-invariant norms.- 4 — Study of the Order Structure on the Set of Ring Norms.- §1. Maximal chains of ring norms.- §2. Generalized ring norms.- §3. The lattice of subalgebras of the algebra End(E).- §4. Characterization of automorphisms.- Brief Comments on the Literature.- References.