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 .
.