Matrix norms and their applications. Operator theory; Bd. 36.

Belitskii, G.; Libuich

ISBN 10: 3764322209 / ISBN 13: 9783764322205

Editore: Basel, Birkhäuser Verlag, 1988

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Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-02027 3764322209 Sprache: Englisch Gewicht in Gramm: 550. Codice articolo 2487865

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Titolo: Matrix norms and their applications. ...

Casa editrice: Basel, Birkhäuser Verlag

Data di pubblicazione: 1988

Legatura: Hardcover

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.