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Matrix Norms and their Applications

  • G. R. Belitskii
  • Yurii I. Lyubich

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

Table of contents

  1. Front Matter
    Pages I-VIII
  2. G. R. Belitskii, Yurii I. Lyubich
    Pages 1-32
  3. G. R. Belitskii, Yurii I. Lyubich
    Pages 33-111
  4. G. R. Belitskii, Yurii I. Lyubich
    Pages 113-156
  5. G. R. Belitskii, Yurii I. Lyubich
    Pages 157-200
  6. Back Matter
    Pages 201-209

About this book

Introduction

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 . .

Keywords

algebra automorphism matrices matrix semigroup spectral theory

Authors and affiliations

  • G. R. Belitskii
    • 1
  • Yurii I. Lyubich
    • 2
  1. 1.Institute of Low TemperaturesKharkov, UkraineUSSR
  2. 2.University of KharkovKharkov, UkraineUSSR

Bibliographic information