Real Function Algebras

Cover......Page 1
Half Title......Page 2
Series Page......Page 4
Title Page......Page 8
Copyright Page......Page 9
Preface......Page 10
Table of Contents......Page 14
 1.1 Elements of Real Banach Algebras......Page 16
 1.2 Commutative Real Banach Algebras......Page 34
 1.3 Real Function Algebras......Page 42
 1.4 Deformations of a Real Function Algebra......Page 54
2. When Does a Real Function Algebra Equal C(X,τ)?......Page 61
 2.1 Analog of Bishop-Machado Theorem......Page 62
 2.2 Antisymmetric Sets and Peak Sets......Page 75
 2.3 Hoffman-Wermer Theorem and Its Analog......Page 84
 2.4 Analog of Wermer\'s Theorem......Page 89
 2.5 Functions that Operate in Re A......Page 94
3. Gleason Parts of a Real Function Algebra......Page 104
 3.1 Analytic and Harmonic Structure......Page 105
 3.2 Characterizations of Gleason Parts......Page 110
 3.3 Parts of the Complexification......Page 130
 3.4 Topological Characterization of Gleason Parts......Page 138
 3.5 Parts, Analyticity, and Harmonicity......Page 145
4. Boundaries for a Real Function Algebra......Page 151
 4.1 Choquet Sets for Subspaces of C(X,τ)......Page 152
 4.2 Boundaries for Subspaces of C(X,τ)......Page 165
 4.3 Choquet Sets and Boundaries for Complex Subspaces of C(X)......Page 169
5. Isometries of Real Function Algebras......Page 179
 5.1 Unit-Preserving Isometries......Page 180
 5.2 Arbitrary Isometries......Page 185
Symbols......Page 190
References......Page 192
Index......Page 198