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Birkhäuser

Matrix Norms and their Applications

  • Book
  • © 1988

Overview

Authors:
  1. G. R. Belitskii

    1. Institute of Low Temperatures, Kharkov, Ukraine, USSR

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    You can also search for this author in PubMed   Google Scholar

  2. Yurii I. Lyubich

    1. University of Kharkov, Kharkov, Ukraine, USSR

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Operator Theory: Advances and Applications (OT, volume 36)

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Operators in Finite-Dimensional Normed Spaces

    • G. R. Belitskii, Yurii I. Lyubich
    Pages 1-32

  3. Spectral Properties of Contractions

    • G. R. Belitskii, Yurii I. Lyubich
    Pages 33-111

  4. Operator Norms

    • G. R. Belitskii, Yurii I. Lyubich
    Pages 113-156

  5. Study of the Order Structure on the Set of Ring Norms

    • G. R. Belitskii, Yurii I. Lyubich
    Pages 157-200

  6. Back Matter

    Pages 201-209
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About this book

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 . .

Authors and Affiliations

  • Institute of Low Temperatures, Kharkov, Ukraine, USSR

    G. R. Belitskii

  • University of Kharkov, Kharkov, Ukraine, USSR

    Yurii I. Lyubich

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