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Kadison R.V., Ringrose J.R. — Fundamentals of the theory of operator algebras (vol. 1) Elementary Theory
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Название: Fundamentals of the theory of operator algebras (vol. 1) Elementary TheoryАвторы: Kadison R.V., Ringrose J.R. Аннотация: These volumes deal with a subject, introduced half a century ago, that
Язык: Рубрика: Математика /Анализ /Функциональный анализ /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1983Количество страниц: 417Добавлена в каталог: 09.04.2005Операции: Положить на полку |
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379 224 338 338 375 321 322 323 324 325 359 360 362 364 320 *Homomorphism 237 *Isomorphism 237 *Subalgebra 237 Adjoint Banach 48 Adjoint Hilbert 102 Adjoint in an algebra with involution 237 Adjoint of an unbounded operator 157 Affiliated operator 342 344 Algebra 187 233 Algebra 237 Algebra * 237 Algebra abelian (commutative) Banach 180 Algebra abelian C* 210 269 Algebra abelian von Neumann 310 Algebra C* 236 Algebra countably decomposable (von Neumann) 338 339 380 Algebra division 180 Algebra finite-dimensional C* 288 Algebra maximal abelian 308 Algebra normed 174 Algebra of bounded operators 102 186 236 298 299 303 309 Algebra of continuous functions 175 210 Algebra of unbounded continuous functions 355 Algebra of unbounded operators 352 355 Algebra self-adjoint 237 282 309 Algebra simple C* 377 Algebra von Neumann 308 Algebra, Banach 41 174 Algebra, multiplication 308 314 340 343 376 380 Algebra, operator 173 304 Algebra, quotient 177 300 Approximate eigenvector 178 179 183 Approximate identity in 191 Approximate identity in C*-algebras 254 293 Approximate identity, increasing, right 254 Approximation theorems Stone — Weierstrass 219 221 235 Approximation theorems, double commutant 326 Approximation theorems, Kaplansky density 329 Archimedian 297 Baire category theorem 60 223 Balanced neighborhood of 0 13 Balanced set 8 Banach algebra 41 174 Banach dual space 44 Banach inversion theorem 61 Banach lattice 297 Banach module 302 Banach space 36 Banach — Orlicz theorem 73 Bessel’s inequality 90 120 Borel measure, regular 53 54 Bound of a linear functional 44 Bound of a linear operator 40 Bounded linear functional 44 Bounded linear operator 41 Bounded multilinear functional 126 Bounded multilinear mapping 131 Bounded set (in a normed space) 36 Boundedly complete lattice see Lattice Bounding projection 351 Bounding sequence 351 C*-algebra 236 C*-algebra simple 377 Cauchy criterion 26 Cauchy — Schwarz inequality 77 215 256 Cayley transform 327 328 Central carrier 332 333 Character of 231 Character of R 192 282 Character of Z 230 Clopen set 222 Closed graph theorem 62 Closure (of an operator) 155 Codimension 2 Commutant 325 Commutation relations 181 Commutator 181 Compact linear operator 165 166 227 Compact self-adjoint operator 166 167 Compact support 201 Complementary subspaces 11 63 88 Complete (linear topological space) 14 Completion of a normed algebra 174 Completion of a normed space 38 Completion of a pre-Hilbert space 80 Complexification of a real Hilbert space 76 161 Complexification of a real linear space 66 Complexification of a real normed space 66 Compression 121 276 Cone 212 245 Conjugate Hilbert space 131 Conjugate-bilinear functional 100 Conjugate-bilinear functional bounded 100 Conjugate-bilinear functional positive 103 Conjugate-bilinear functional symmetric 103 Conjugate-linear operator 15 65 Convergence of nets in a locally convex space 25 Convergence of series in a normed space 38 Convergence of sums in a locally convex space 25 Convex combination (finite) 3 Convex hull (of a set) 4 Convex hull closed 31 Convex set 3 Convolution 187 230 231 Core (for an unbounded operator) 155 349 Countably decomposable projection 338 340 380 Countably decomposable von Neumann algebra 338 339 380 Cyclic projection 336 Cyclic representation 276 278 279 Cyclic vector 276 Definite inner product 76 Definite state 289 Derivation 301 302 Dimension (of a Hilbert space) 93 Direct sum of Hilbert spaces 121 123 Direct sum of operators 122 124 Direct sum of representations 281 Direct sum of von Neumann algebras 336 Division algebra 180 Double commutant theorem 326 Dual group of 231 Dual group of R 192 Dual group of Z 230 Dual space algebraic 2 Dual space Banach 44 Dual space continuous 30 43 Dual space second 43 45 Eigenvalue 109 Eigenvector 108 Eigenvector approximate 178 179 183 Equivalence of function representations 263 Equivalence of representations 280 Essential range of a measurable function 380 Essential range of an 185 Essential representation 282 Essential supremum 52 Essentially bounded 52 Evaluation functional 211 Extension by continuity 14 15 Extension of pure states 266 296 Extension of states 266 296 Extension theorems see Hahn — Banach theorems Extreme point 31 32 33 34 163 164 373 Extremely disconnected space 222 223 224 310 322 324 344 349 373 374 375 376 Face 32 Factor 308 Factorization 2 42 Factors through 2 42 Faithful representation 275 281 Faithful state 288 Finite diagonal block (of a matrix) 154 Finite-dimensional space 22 23 24 Finite-dimensional subspace 22 23 24 First category (set of) 322 Fourier coefficients 95 Fourier series 95 Fourier transform 187 197 368 Fourier transform for 201 Fourier transform inversion of 198 199 Function calculus Borel (for bounded normal operators) 319 321 322 324 377 Function calculus Borel (for unbounded normal operators) 340 360 361 363 364 366 380 Function calculus continuous 239 240 271 272 273 274 340 Function calculus holomorphic 206 Function calculus uniqueness 273 322 362 Function representation 263 264 Function representation equivalence of 263 Function representation of a Banach lattice 297 Function representation of an abelian C*-algebra 270 Function representation separating 263 Functional conjugate-bilinear 100 Functional linear 2 Functional real-linear 7 Functional sublinear 8 9 Functional support 9 65 Gelfand — Neumark theorem 275 281 Generalized nilpotent 205 225 226 227 Generating set of vectors 336 337 Generating vector for a cyclic projection 336 Generating vector for a representation 276 Generating vector for a von Neumann algebra 336 338 379 380 GNS construction 279 GNS construction (essential) uniqueness of 279 Gram — Schmidt orthogonalization process 94 Graph (of an operator) 62 155 Hahn — Banach theorems, extension type 7 9 10 21 22 44 Hahn — Banach theorems, separation type 4 7 20 21 Hahn — Jordan decomposition 219 258 259 265 290 Half-space (closed or open) 4 Hermite polynomials 97 Hermitian linear functional on a C*-algebra 255 Hermitian linear functional on C(X) 215 Hilbert space 79 Hilbert space conjugate 131 Hilbert space, isomorphism 93 103 104 Hilbert space, pre-Hilbert space 79 80 81 Hilbert — Schmidt functional 127 Hilbert — Schmidt mapping (weak) 131 Hilbert — Schmidt operator 141 Hoelder’s inequality 71 188 Holomorphic function (Banach-space valued) 203 Holomorphic function calculus 206 Hull closed convex 31 Hull convex 4 Hull of a set 211 Hyperplane 4 Ideal in 187 190 Ideal in a Banach algebra 177 Ideal in a C*-algebra 251 252 254 277 300 301 Ideal in C(X) 210 Ideal maximal 177 180 210 Idempotent 11 208 Initial topology 13 Inner product 75 76 79 Inner product definite 76 79 277 Inner product positive definite 76 Inner product space 76 Internal point 4 Intersection (of projections) 111 Invariant mean 224 Invariant subspace 121 Invariant subspace in 233 Invariant subspace in Hilbert space 121 Inverse (in a Banach algebra) 176 Inversion theorem Banach 61 Inversion theorem for Fourier transforms 199 Invertible element (in a Banach algebra) 176 Involution 236 Irreducibility algebraic 330 332 Irreducibility topological 330 331 332 Isometric isomorphism 36 Isometric isomorphism natural, from 45 Isometric isomorphism of C*-algebras 242 Isometric isomorphism of function calculus 240 Jacobi polynomials 97 Kaplansky density theorem 329 Kernel left, of a state 278 Kernel of a representation 276 Kernel of an ideal in C(X) 211 Krein — Milman theorem 32 Laguerre polynomials 97 Lattice 214 215 298 Lattice Banach 297 Lattice boundedly complete 222 223 374 375 376 Lattice, sublattice 235 Legendre polynomials 97 Linear combination (finite) 1 Linear dependence 1 Linear functional 2 Linear functional bounded 44 Linear functional weak* continuous 31 Linear functional weakly continuous 29 30 Linear independence 1 Linear operator see Operator Unbounded Linear order isomorphism 214 Linear topological space 12 Linear transformation see Operator Unbounded Locally compact (locally convex space) 24 Locally convex space 16 Locally convex space finite-dimensional 23 24 Locally convex space locally compact 24 Locally convex topology 16 Locally finite group 224 Matrix with operator entries 148 Matrix with scalar entries 147 Maximal abelian algebra 308 Maximal ideal 177 180 187 190 210 Meager set 322 375 Minimal projection 309 Minkowski’s inequality for integrals 53 Minkowski’s inequality for sums 50 Multilinear functional 180 183 Multilinear mapping 131 Multiplication algebra 308 314 340 343 376 380 Multiplication operator 106 107 108 109 117 185 315 341 342 343 344 Multiplicative linear functional 180 183 187 269 Multiplicative linear functional on 231 Multiplicative linear functional on 193 Multiplicative linear functional on 232 Multiplicative linear functional on 224 Multiplicative linear functional on C(X) 211 213 Multiplicity (of an eigenvalue) 167 227 Natural image of 45 Neighborhoods balanced 13 18 Neighborhoods in a linear topological space 13 Neighborhoods in a locally convex space 17 18 Neighborhoods in a normed space 35 Neighborhoods in a weak topology 28 Neighborhoods in the strong-operator topology 113 Neighborhoods in the weak* topology 31 Neighborhoods in the weak-operator topology 305 Nilpotent 205 Non-singular (element of a Banach algebra) 176 Norm 8 35
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