CHAPTER 1 - OPERATORS IN FINITE-DIMENSIONAL NORMED SPACES 1 SSl. Norms of vectors, linear functionals, and linear operators. 1 SS 2. Survey of spectral theory 14 SS 3. Spectral radius . 17 SS 4. One-parameter groups and semigroups of operators. 25 Appendix. Conditioning in general computational problems 28 CHAPTER 2 - SPECTRAL PROPERTIES OF CONTRACTIONS 33 SSl. Contractive operators and isometries. 33 SS2. Stability theorems. 46 SS3. One-parameter semigroups of contractions and groups of isometries. 48 SS 4. The boundary spectrum of extremal contractions. 52 SS5. Extreme points of the unit ball in the space of operators. 64 SS6. Critical exponents. 66 SS7. The apparatus of functions on graphs. 72 SS8. Combinatorial and spectral properties of t -contractions . 81 00 SS9. Combinatorial and spectral properties of 96 nonnegative matrices. SS10. Finite Markov chains. 102 SSll. Nonnegative projectors. 108 VI CHAPTER 3 - OPERATOR NORMS . 113 SSl. Ring norms on the algebra of operators in E 113 SS2. Characterization of operator norms. 126 SS3. Operator minorants. . . . . . 133 SS4. Suprema of families of operator norms 141 SS5. Ring cross-norms . . 150 SS6. Orthogonally-invariant norms. 152 CHAPTER 4 - STUDY OF THE ORDER STRUCTURE ON THE SET OF RING NORMS . 157 SSl. Maximal chains of ring norms. 157 SS2. Generalized ring norms. 160 SS3. The lattice of subalgebras of the algebra End(E) 166 SS 4 . Characterization of automorphisms 179 201 Brief Comments on the Literature 205 References . .
