Matrix norms and their applications
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Bibliographic Information
Matrix norms and their applications
（Operator theory : advances and applications, v. 36）
Birkhäuser, 1988
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- : sw
- Other Title
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Normy matrit︠s︡ i ikh prilozhenii︠a︡
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
swdc19:512.9/4122070105520
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Note
Bibliography:p. 205-209
Description and Table of Contents
Description
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 . .
Table of Contents
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.
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