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AuthorBelitskii, G. R. author
TitleMatrix Norms and their Applications [electronic resource] / by G. R. Belitskii, Yurii I. Lyubich
ImprintBasel : Birkhรคuser Basel, 1988
Connect tohttp://dx.doi.org/10.1007/978-3-0348-7400-7
Descript VIII, 210 p. online resource

SUMMARY

CHAPTER 1 - OPERATORS IN FINITE-DIMENSIONAL NORMED SPACES 1 ยงl. Norms of vectors, linear functionals, and linear operators. 1 ยง 2. Survey of spectral theory 14 ยง 3. Spectral radius . 17 ยง 4. One-parameter groups and semigroups of operators. 25 Appendix. Conditioning in general computational problems 28 CHAPTER 2 - SPECTRAL PROPERTIES OF CONTRACTIONS 33 ยงl. Contractive operators and isometries. 33 ยง2. Stability theorems. 46 ยง3. One-parameter semigroups of contractions and groups of isometries. 48 ยง 4. The boundary spectrum of extremal contractions. 52 ยง5. Extreme points of the unit ball in the space of operators. 64 ยง6. Critical exponents. 66 ยง7. The apparatus of functions on graphs. 72 ยง8. Combinatorial and spectral properties of t -contractions . 81 00 ยง9. Combinatorial and spectral properties of 96 nonnegative matrices. ยง10. Finite Markov chains. 102 ยงll. Nonnegative projectors. 108 VI CHAPTER 3 - OPERATOR NORMS . 113 ยงl. Ring norms on the algebra of operators in E 113 ยง2. Characterization of operator norms. 126 ยง3. Operator minorants. . . . . . 133 ยง4. Suprema of families of operator norms 141 ยง5. Ring cross-norms . . 150 ยง6. Orthogonally-invariant norms. 152 CHAPTER 4 - STUDY OF THE ORDER STRUCTURE ON THE SET OF RING NORMS . 157 ยงl. Maximal chains of ring norms. 157 ยง2. Generalized ring norms. 160 ยง3. The lattice of subalgebras of the algebra End(E) 166 ยง 4 โ{128}ข Characterization of automorphisms 179 201 Brief Comments on the Literature 205 References .


CONTENT

1 โ{128}{148} Operators in Finite-Dimensional Normed Spaces -- ยง1. Norms of vectors, linear functionals, and linear operators -- ยง2. Survey of spectral theory -- ยง3. Spectral radius -- ยง4. One-parameter groups and semigroups of operators -- Appendix. Conditioning in general computational problems -- 2 โ{128}{148} Spectral Properties of Contractions -- ยง1. Contractive operators and isometries -- ยง2. Stability theorems -- ยง3. One-parameter semigroups of contractions and groups of isometries -- ยง4. The boundary spectrum of extremal contractions -- ยง5. Extreme points of the unit ball in the space of operators -- ยง6. Critical exponents -- ยง7. The apparatus of functions on graphs -- ยง8. Combinatorial and spectral properties of l?-contractions -- ยง9. Combinatorial and spectral properties of nonnegative matrices -- ยง10. Finite Markov chains -- ยง11. Nonnegative projectors -- 3 โ{128}{148} Operator Norms -- ยง1. Ring norms on the algebra of operators in E -- ยง2. Characterization of operator norms -- ยง3. Operator minorants -- ยง4. Suprema of families of operator norms -- ยง5. Ring cross-norms -- ยง6. Orthogonally-invariant norms -- 4 โ{128}{148} Study of the Order Structure on the Set of Ring Norms -- ยง1. Maximal chains of ring norms -- ยง2. Generalized ring norms -- ยง3. The lattice of subalgebras of the algebra End(E) -- ยง4. Characterization of automorphisms -- Brief Comments on the Literature -- References


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