دانلود کتاب Direct Integral Theory

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Cover ......Page 1
Half Title ......Page 2
Title Page ......Page 8
Copyright Page ......Page 9
Table of Contents ......Page 14
Preface ......Page 10
1: Definitions......Page 18
2: Borel Spaces and Functions......Page 20
3: Borel Spaces and Equivalence Relations......Page 24
4: Borel Spaces and Measures......Page 26
Historical Comments......Page 29
5: Hilbert Space-Valued L2-Spaces......Page 32
6: Operators on Hilbert Space-Valued L2 -Spaces......Page 34
7: Fields of Hilbert Spaces and Operators......Page 39
8: The Construction of Coherences......Page 44
9: Direct Integral Decompositions......Page 47
10: Examples......Page 51
Historical Comments......Page 59
11: Definitions and Some Elementary Properties......Page 62
12: Equivalence, Existence and Uniqueness of Direct Integral Decompositions......Page 64
13: Maximal and Central Decompositions......Page 68
14: Some Applications......Page 71
15: Examples......Page 72
Historical Comments......Page 79
16: Hausdorff Metrics......Page 80
17: The Effros Borel Structure......Page 84
18: Definitions and Some Elementary Properties......Page 91
19: Some Further Properties......Page 93
20: Examples......Page 97
Historical Comments......Page 99
21: The Statements of Two Theorems......Page 102
22: Partial Proof of Theorem 21.1......Page 104
23: Proof of Theorem 21.2......Page 110
24: Some Technical Lemmas......Page 116
25: The Completion of the Proof of Theorem 21.1......Page 129
Historical Comments......Page 130
26: The Dual and the Quasi-Dual......Page 132
27: Measures on the Dual and Representations......Page 137
28: Measures on the Quasi-Dual and Representations......Page 143
Historical Comments......Page 152
Appendix A: Von Neumann Algebras......Page 156
Appendix B: Representations of Involutive Banach Algebras......Page 162
Appendix C: Representations of Locally Compact Groups......Page 168
References......Page 174
Index of Notation ......Page 178
Index ......Page 180