Spectral Theory

Title......Page 1
Preface......Page 7
Contents......Page 11
1. On structure,......Page 15
2. The axioms,......Page 16
3. Linear functionals,......Page 22
4. The canonical map,......Page 27
5. Subspaces and orthogonality,......Page 28
6. The Hahn-Banach theorem,......Page 30
7. Other topologies,......Page 35
8. Examples and exercises,......Page 40
1. Preliminaries,......Page 44
2. The adjoint transformation,......Page 48
3. The boundedness of the inverse transformation,......Page 49
4. Closed transformations,......Page 54
5. The uniform boundedness principle,......Page 57
6. Projections,......Page 58
7. Topologies for transformations,......Page 63
8. On range and null-space,......Page 64
9. The mean-ergodic theorem,......Page 66
1. Definition,......Page 69
2. Linear functionals,......Page 74
3. Orthonormal sets,......Page 77
4. Unbounded transformations and their adjoints,......Page 81
5. Projections,......Page 84
6. Resolutions of the identity,......Page 86
7. Unitary transformations,......Page 91
8. Examples and exercises,......Page 93
1. The setting,......Page 98
2. The spectrum,......Page 101
3. Integration procedures,......Page 103
4. The fundamental projections,......Page 104
5. A special case,......Page 111
6. The spectral radius,......Page 113
7. Analytic functions of operators,......Page 114
1. Preliminary discussion,......Page 118
2. Positive operators,......Page 119
3. The point spectrum,......Page 122
4. The partition into pure types,......Page 124
5. The continuous spectrum,......Page 127
1. Introduction,......Page 134
2. Definitions and examples,......Page 135
3. The regular representation,......Page 137
4. Reducibility and idempotents,......Page 139
5. Algebras which are fields,......Page 140
6. Ideals,......Page 142
7. Quotient algebras,......Page 1441
8. Homomorphisms and maximal ideals,......Page 148
9. The radical,......Page 153
10. The representation theory,......Page 155
11. Illustrative examples and applications,......Page 157
Selected References,......Page 165
Index,......Page 167