K-Theory for Operator AlgebrasK-theory has helped convert the theory of operator algebras from a simple branch of functional analysis to a subject with broad applicability throughout mathematics, especially in geometry and topology, and many mathematicians of diverse backgrounds must learn the essential parts of the theory. This book is the only comprehensive treatment of K-theory for operator algebras, and is intended to help students, non specialists, and specialists learn the subject. This first paperback printing has been revised and expanded and contains an updated reference list. This book develops K-theory, the theory of extensions, and Kasparov's bivariant KK-theory for C*-algebras. Special topics covered include the theory of AF algebras, axiomatic K-theory, the Universal Coefficient Theorem, and E-theory. Although the book is technically complete, motivation and intuition are emphasized. Many examples and applications are discussed. |
Contents
III | 1 |
IV | 3 |
V | 4 |
VII | 5 |
IX | 7 |
X | 9 |
XI | 10 |
XII | 11 |
CVI | 122 |
CVIII | 123 |
CIX | 125 |
CX | 126 |
CXI | 128 |
CXII | 129 |
CXIII | 131 |
CXV | 132 |
XIV | 12 |
XV | 13 |
XVI | 15 |
XVII | 16 |
XVIII | 17 |
XIX | 18 |
XX | 19 |
XXI | 20 |
XXIV | 21 |
XXV | 22 |
XXVI | 24 |
XXVII | 25 |
XXVIII | 27 |
XXIX | 28 |
XXX | 29 |
XXXII | 30 |
XXXIII | 31 |
XXXIV | 32 |
XXXVII | 33 |
XXXVIII | 34 |
XXXIX | 36 |
XLI | 38 |
XLII | 39 |
XLIII | 40 |
XLIV | 41 |
XLV | 42 |
XLVI | 45 |
XLVII | 48 |
XLIX | 49 |
LI | 51 |
LII | 52 |
LIII | 53 |
LIV | 55 |
LV | 59 |
LVI | 61 |
LVII | 62 |
LVIII | 64 |
LX | 65 |
LXI | 67 |
LXII | 68 |
LXIII | 70 |
LXIV | 71 |
LXV | 72 |
LXVI | 74 |
LXVII | 75 |
LXVIII | 76 |
LXIX | 77 |
LXX | 78 |
LXXI | 79 |
LXXII | 83 |
LXXIII | 86 |
LXXIV | 92 |
LXXVI | 93 |
LXXVII | 94 |
LXXVIII | 95 |
LXXX | 96 |
LXXXI | 97 |
LXXXII | 98 |
LXXXIII | 100 |
LXXXV | 103 |
LXXXVI | 104 |
LXXXVII | 105 |
LXXXIX | 107 |
XC | 108 |
XCII | 109 |
XCIII | 110 |
XCV | 111 |
XCVII | 113 |
XCVIII | 114 |
C | 116 |
CII | 118 |
CIII | 119 |
CIV | 120 |
CV | 121 |
CXVII | 134 |
CXIX | 135 |
CXXI | 137 |
CXXII | 139 |
CXXIII | 143 |
CXXIV | 147 |
CXXV | 149 |
CXXVI | 152 |
CXXVII | 155 |
CXXVIII | 158 |
CXXX | 161 |
CXXXII | 163 |
CXXXIII | 166 |
CXXXVI | 169 |
CXXXVII | 178 |
CXXXVIII | 179 |
CXXXIX | 181 |
CXL | 183 |
CXLI | 184 |
CXLII | 185 |
CXLIII | 187 |
CXLIV | 189 |
CXLV | 190 |
CXLVI | 193 |
CXLVII | 195 |
CXLVIII | 198 |
CXLIX | 199 |
CL | 200 |
CLI | 201 |
CLII | 204 |
CLIII | 205 |
CLIV | 206 |
CLV | 207 |
CLVI | 208 |
CLVII | 209 |
CLVIII | 210 |
CLIX | 211 |
CLX | 213 |
CLXII | 215 |
CLXIII | 217 |
CLXIV | 219 |
CLXV | 220 |
CLXVI | 222 |
CLXVII | 223 |
CLXVIII | 224 |
CLXIX | 225 |
CLXX | 226 |
CLXXI | 227 |
CLXXII | 230 |
CLXXIII | 232 |
CLXXV | 234 |
CLXXVI | 235 |
CLXXVIII | 236 |
CLXXIX | 238 |
CLXXX | 239 |
CLXXXII | 240 |
CLXXXIV | 243 |
CLXXXVII | 244 |
CLXXXVIII | 245 |
CLXXXIX | 248 |
CXCI | 253 |
CXCII | 255 |
CXCIII | 257 |
CXCIV | 258 |
CXCV | 260 |
CXCVI | 261 |
CXCVII | 265 |
CXCIX | 268 |
CC | 270 |
CCI | 277 |
CCII | 279 |
297 | |
Other editions - View all
Common terms and phrases
A₁ abelian groups asymptotic morphism Aut(A automorphism B₁ Banach algebra Blackadar Bott Periodicity C(S¹ C₁ Co(R cohomology commutative compact perturbation COROLLARY corresponding countable covariant crossed products Cuntz defined DEFINITION denoted dimension group direct sum E₁ equivalence classes equivalence relation equivariant essential example Ext(A function functor graded C*-algebras Hilbert B-module Hilbert modules homology theory homomorphism idempotents identity index theorem induced inductive limit injective intersection product invertible elements isometry K-groups K-theory K₁(A K₁(B Kasparov module Kasparov product KK-equivalence KK(A KKoh Ko(A Ko(B LEMMA locally compact natural nonunital nuclear C*-algebras o-unital ordered group projection PROOF PROPOSITION quasihomomorphism quotient map Rosenberg Schochet self-adjoint semigroup semisplit separable C*-algebras short exact sequence Skandalis space stable stably finite structure subgroup surjective tensor product Thom isomorphism topology trivially graded unital C*-algebra unitary vector bundle