Introduction to function algebras

Title page  ......Page 1
A Note from the Publisher  ......Page 2
Copyright  ......Page 3
Introduction  ......Page 4
Table of contents  ......Page 8
1-1 Function algebras  ......Page 10
1-2 Banach algebras  ......Page 17
1-3 The maximal ideal spaces of some examples  ......Page 38
1-4 The functional calculus  ......Page 55
1-5 Analytic structure  ......Page 65
1-6 Point derivations  ......Page 72
2-1 Representing and annihilating measures  ......Page 88
2-2 The Choquet boundary  ......Page 96
2-3 Peak points  ......Page 105
2-4 Peak sets and interpolation  ......Page 111
2-5 Representing measures and the Jensen inequality  ......Page 123
2-6 Representing measures and Schwarz\'s lemma  ......Page 136
2-7 Antisymmetric algebras  ......Page 145
2-8 The essential set  ......Page 153
3-1 Preliminaries  ......Page 158
3-2 Annihilating measures for R(X)  ......Page 167
3-3 Representing measures for R(X)  ......Page 179
3-4 harmonic functions  ......Page 188
3-5 The algebras A(X) and Ax  ......Page 204
4-1 Dirichlet algebras  ......Page 216
4-2 Annihilating measures  ......Page 224
4-3 Applications  ......Page 237
4-4 Analytic structure in the maximal ideal space  ......Page 252
Appendix: Cole\'s Counterexample to the Peak Point Conjecture  ......Page 264
Bibliography  ......Page 272
Mathematics lecture note series  ......Page 283