Gerard J. Murphy0125113609, 9780125113601
Table of contents :
Front cover……Page 1
Title page……Page 3
Date-line……Page 4
Dedication……Page 5
Contents……Page 7
Preface……Page 9
1.1. Banach Algebras……Page 11
1.2. The Spectrum and the Spectral Radius……Page 15
1.3. The Gelfand Representation……Page 23
1.4. Compact and Fredholm Operators……Page 28
Exercises……Page 40
Addenda……Page 44
2.1. C$^ast$-Algebras……Page 45
2.2. Positive Elements of C$^ast$-Algebras……Page 54
2.3. Operators and Sesquilinear Forms……Page 58
2.4. Compact Hilbert Space Operators……Page 63
2.5. The Spectral Theorem……Page 76
Exercises……Page 83
Addenda……Page 85
3.1. Ideals in C$^ast$-Algebras……Page 87
3.2. Hereditary C$^ast$-Subalgebras……Page 93
3.3. Positive Linear Functionals……Page 97
3.4. The Gelfand-Naimark Representation……Page 103
3.5. Toeplitz Operators……Page 106
Exercises……Page 117
Addenda……Page 120
4.1. The Double Commutant Theorem……Page 122
4.2. The Weak and Ultraweak Topologies……Page 134
4.3. The Kaplansky Density Theorem……Page 139
4.4. Abelian Von Neumann Algebras……Page 143
Exercises……Page 146
Addenda……Page 148
5.1. Irreducible Representations and Pure States……Page 150
5.2. The Transitivity Theorem……Page 159
5.3. Left Ideals of C$^ast$-Algebras……Page 163
5.4. Primitive Ideals……Page 166
5.5. Extensions and Restrictions of Representations……Page 172
5.6. Liminal and Postliminal C$^ast$-Algebras……Page 177
Exercises……Page 181
Addenda……Page 182
6.1. Direct Limits of C$^ast$-Algebras……Page 183
6.2. Uniformly Hyperfinite Algebras……Page 188
6.3. Tensor Products of C$^ast$-Algebras……Page 194
6.4. Minimality of the Spatial C$^ast$-Norm……Page 206
6.5. Nuclear C$^ast$-Algebras and Short Exact Sequences……Page 220
Exercises……Page 223
Addenda……Page 226
7.1. Elements of K-Theory……Page 227
7.2. The K-Theory of AF-Algebras……Page 231
7.3. Three Fundamental Results in K-Theory……Page 239
7.4. Stability……Page 251
7.5. Bott Periodicity……Page 255
Exercises……Page 272
Addenda……Page 274
Appendix……Page 277
Notes……Page 287
References……Page 289
Notation Index……Page 291
Subject Index……Page 293
Back cover……Page 297
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