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Bratteli O., Robinson D.W. — Operator Algebras and Quantum Statistical Mechanics (vol. 1)
Bratteli O., Robinson D.W. — Operator Algebras and Quantum Statistical Mechanics (vol. 1)



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Название: Operator Algebras and Quantum Statistical Mechanics (vol. 1)

Авторы: Bratteli O., Robinson D.W.

Аннотация:

This is the first of two volumes presenting the theory of operator algebras with applications to quantum statistical mechanics. The authors' approach to the operator theory is to a large extent governed by the dictates of the physical applications. The book is self-contained and most proofs are presented in detail, which makes it a useful text for students with a knowledge of basic functional analysis. The introductory chapter surveys the history and justification of algebraic techniques in statistical physics and outlines the applications that have been made.
The second edition contains new and improved results. The principal changes include: A more comprehensive discussion of dissipative operators and analytic elements; the positive resolution of the question of whether maximal orthogonal probability measure on the state space of C-algebra were automatically maximal along all the probability measures on the space.


Язык: en

Рубрика: Физика/Термодинамика, статистическая физика/Квантовые методы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 2002

Количество страниц: 505

Добавлена в каталог: 29.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$G_{\Gamma}$-Abelian      414 415 417 419 420 428 433 434 436 455 463
Absolute value      34
Action, continuous      393 400
Action, dual      140 149 375
Action, ergodic      137 142
Action, free      137 142
Action, transitive      464
Adjoint      19
Akemann      460
Akemann and Pedersen      309
Alaoglu — Birkhoff mean ergodic theorem      378
Albert      7
Alfsen      8
Algebra at infinity      122 123 126 156 318 370 373 440 453 454
Algebra nuclear      144 151
Algebra operator      3 136 439
Algebra semisimple      306
Algebra, $\mathcal{L,B}(\mathfrak{H})$      21 72 129 130 131 133 246 247 306 307 309 352
Algebra, $\mathcal{L}(\mathfrak{H})$      11 20 38 68 69 72 85 96 106 124 129 131 225 226 245 246 247 248 258 292 305 306 309 321 356 379 398
Algebra, $\sigma$-finite von Neumann      84 151 155
Algebra, abelian      19 35 58 62 63 83
Algebra, antiliminal      352
Algebra, B*-      152
Algebra, Banach      19 20 25 137 152 430
Algebra, Borchers      463
Algebra, C*-      3 19 20 25
Algebra, commutant      122 126 370
Algebra, commutative      19 21 61 154
Algebra, direct integral      445 446
Algebra, finite von Neumann      147
Algebra, fixed point      310 313
Algebra, function      21
Algebra, group      249
Algebra, hyperfinite von Neumann      150 151
Algebra, infinite von Neumann      147
Algebra, Jordan      7 16
Algebra, local      11 118
Algebra, maximal abelian von Neumann      320 350 361 367 391 417 420 447 448 452
Algebra, multiplier      309
Algebra, n-dimensionally homogeneous      351 459 460
Algebra, normed      20
Algebra, prime      310
Algebra, properly infinite von Neumann      135 141 147
Algebra, purely infinite von Neumann      147
Algebra, quasi-local      11 81 118 120 121 122 124 125 128 129 133 134 135 156 219 289 317 321 352 373 450 453 454 460
Algebra, quotient      39 40 41 43
Algebra, reduced von Neumann      155
Algebra, self-adjoint      19
Algebra, semifinite von Neumann      147 148 150
Algebra, simple      7 24 44 133 134 142
Algebra, topological      7
Algebra, type I C*-      151
Algebra, UHF (Uniformly hyperfinite)      129 156 236 268 306 307 308 351 353 405
Algebra, von Neumann      3 65 70 75 76
Algebra, W*-      3 155 305
Algebras, measurable family of      445
Analysis, abelian harmonic      140
Analytic continuation      25
Analyticity, strong      99 155 178
Analyticity, weak      99 155 178
Annihilator      408 412 417 438 429 436 455
Approximation theory      202 290 299 304
Araki      152 155 156
Arnold and Avez      463
Arveson      152 308 309
Asymptotic abelianness      14 340 341 342 343 380 406 414 461 462 463 see
Asymptotically abelian, weakly      403
Asymptotically abelian, weakly ... in mean      403
Automorphism      12 13 16 44 56 96 97 102 108 139 209—313 374—452
Automorphism, anti-      209
Automorphism, inner      141 148 149 225 249 283 293 294 295 300 305 310 312 313
Automorphism, Jordan      211 225 226 227 229 230 231 277
Automorphism, modular      see "modularautomorphism"
Automorphism, order      211
Avez      464
Baire measure      see "measure Baire"
Baire set      318 322 324 331 332 333 350 353 354 355 356 357 367 458
Baire structure      352
Banach      154
Barycenter      318—350 359—390 424 426
Base (of a cone)      334
Bauer maximum principle      331
Bicommutant      72
Bidual      130 217
Bishop and de Leeuw      458 459
Bohr      3
Bohr compactification      435 436
Boost      302 309
Borchers      308 309 311 312
Borchers and Yngvason      463
Borel automorphism      288
Borel cross section      295
Borel function      5 295
Borel map      see "map Borel"
Borel measure      see "measure Borel"
Borel set      5 289 295 318 322 331 333 338 340 343 350 354 355 356 357 412 458 460 463
Borel structure      350 440 446
Bose gas      14
Bound, greatest lower      323 334 335 369 385
Bound, greatest lower least upper      76 78 79 121 323 369 385
boundary conditions      160
Boundary conditions, set      326
Bratteli and Kishimoto      304 311
Bratteli and Kishimoto and Haagerup      311
Bratteli and Kishimoto and Robinson      305
Bratteli, Herman and Robinson      304
Bucholz and Roberts      304 311
Butzer      304
C*-norm      20
Cantor — Bernstein argument      81
Cantor — Bernstein set      306 308
Cauchy estimates      178
Cauchy representation      242
Cauchy transform      25
Cayley numbers      7
Center      71 123 125 126 147 295 317 364 370 389 390 445 446 453
Center of mass      318
Central sequence      309
centralizer      279 280 282 284
Chaiken      9
CHARACTER      61 62 63 139 249 250 251
Chernoff      303 304
Chi      306
Choquet      458 459 460
Circled subset      98 163
Classification of C*-algebras      145 151
Classification of C*-algebras of factors      145
Cluster property      118 128 156 393 398 400 401 404 406 420 429 438 440
Cluster property, multiple      402
Cocycle      141 298 312
Cocycle identity      294 297
Cocycle, one-      294 296 299
Cocycle, two-      296 297 299
Cohomology      312
Cohomology of $\mathbb{R}$ is trivial      307
Commutant      47 57 58 71 85 305 317 319 320 339 370 375 426 431 433 445
Commutant, Commutation relations, canonical      4
Commutant, Commutation relations, Weyl      6
Commute strongly      278 279
Conditional expectation      150
Cone, apex of      334
Cone, base of      334
Cone, convex      34 36 83 334
Cone, dual      104
Cone, hereditary      145
Cone, homogeneous      156
Cone, natural      102 106 107 108 147 155 156 226 227 228 229 232 264 299 305 369
Cone, orientable      156
Cone, pointed      105
Cone, self-dual (self-polar)      83 84 97 104 105 145 156
Connes      155 156 308 310 312
Connes and Takesaki      310
Construction, GNS      153 220
Continuous, $\sigma(X,F)$      97 98 100 164—184 194 202 204 219 250 252 253 254 256 303
Continuous, $\tau(X,F)$      168 184
Continuous, Hoelder      206 290
Continuous, strongly      97 160 164 169 226 232 240 257 261 265 267 268 299 300
Continuous, uniformly (norm)      97 160 161 233 256 261 263 264
Continuous, weakly      97 136 160 164 169 226 258
Continuous, weakly* ($\sigma$-weakly)      160 169 226 233 257 259 261 267 285 288 294 296 299 302 312
Contraction      161 169 170 177 178 194 196
Convolution      249 252
Cook      8
Core      167 182 188 191 196 267 270 274 275 277 278 282 283 284 286 287 289 290 308
Cross section      295
Cross-norm      144
Crossed product      136 137 138 139 141 284 310
Crossed product skew      141
Cuntz      306
Cyclic projector      46
Cyclic subset      85 86
Cyclic subspace      46
Cyclic vector      45 46 86 88 109
Dang Ngoc and Guichardet      462
de Leeuw      303 304 458 459
Decomposition      14 32 45 105 106 117 121 343 379 415 424
Decomposition at infinity      317 465
Decomposition of positive linear functionals over *-algebras      463
Decomposition of representations      317 440 446
Decomposition of States      129 317 449 450 459 460
Decomposition, almost periodic      430 437
Decomposition, barycentric      321 324 335 350 356 367 447 458 461
Decomposition, central (factor)      317 358 370 423 440 447 460
Decomposition, direct integral      450 453
Decomposition, direct sum      45
Decomposition, ergodic      318 374 380 386 390 393 423 429 440 461 462 463
Decomposition, extremal      317 318 358 359 367 440 447
Decomposition, finite      319
Decomposition, Jordan      216 219 222 236 305 369
Decomposition, orthogonal      36
Decomposition, polar      38 72 87 89 90 92 107 108 109 112 116 130 152 287 291 292 302 312 396 397 419
Decomposition, property of a lattice      336
Decomposition, spatial      439 447 449 450 451 455 465
Decomposition, spectral      95 251 320 407
Decomposition, theory      317 459
Dell' Antonio      9
Density matrix      76 85 106 124 127 129 130 131
Derivation      160 233—249 265—268 282 286 292 306 307 309
Derivation theorem      262
Derivation, bounded      235 236 246 249 262 263 290 291 300 301
Derivation, everywhere defined      235 262 263 306
Derivation, implementation of a      269
Derivation, inner      305
Derivation, nonclosable      306
Derivation, norm-closed      235—245 306
Derivation, normal      308
Derivation, spatial      268 270 271 272 274 287
Derivation, symmetric      233
Diffeomorphism      159
Differentiable, strongly      203
Differentiable, uniformly      161 162
Differentiable, weakly*      203
Digernes      311
Direct integral      439 440 450 454
Direct sum      45 46 60 439
Dixmier      152 312
Doplicher and Kastler      463 464
Doplicher and Kastler and Robinson      461
Doplicher and Kastler and Robinson and Stormer      462
Douglas      460
Dual      48 51 53 62 76 130 170 204 216 219 305 317 350
Dual group      see "group dual"
Duality      126 130 169 209
Dunford      155
Dye      305
Dynamical flow      159
Dynamical system      13 136 137
Dynamical system, C*      136 137 139 142 310
Dynamical W*      136 137 138 140 142 310
Dynamics      159 160
Effros      465
Element (entire) analytic      97 99 101 115 178—183 231 265—267 272 293
Element (entire) identity      see "identity"
Element (entire) odd      121
Element (entire), even      121
Element (entire), invertible      25 38 213
Element (entire), isometric      28
Element (entire), normal      28
Element (entire), positive      7 32 38 215 276
Element (entire), quasi-analytic      311
Element (entire), self-adjoint      28
Element (entire), unitary      28 38 72 97 107 110 111 141 214 384 395 417 418
Elliott      152 306 309 311
Envelope, lower      326 327
Envelope, upper      326 327 328 335 338
Equicontinuity      167 185
Equicontinuous, $\tau(X,F)$      168 174 204
Equivalence, physical      14
Equivalence, quasi      79 80 81 82 128 370 395 452
Equivalence, unitary      48 56 79 80 151 283 396 429 442 450 457
Ergodic theory      13 401 423 decomposition state"
Ergodicity, central      395
Extension, canonical      52 58 60
Extension, state      52
Extremal point      53 57 317 321 325 327 330 331 350 353 405 425 464
Face      319 321 355 369 372 373 385 428 432 436 440 447 449 450 454 455 464
Face, stable      333 334 353 354 355 356 373 377 378
Factor      71 127 142 149 151 267 277 310 312 355 356 358 423 446 448
Factor, finite      134
Factor, hyperfinite      137 142 150 151 305
Factor, infinite      148
Factor, Krieger      142 151
Factor, purely infinite      148
Factor, semifinite      148
Factor, state      see "state factor"
Factor, type $III_{0}$      150
Factor, type $III_{1}$      150
Factor, type $III_{A}$      150 151
Factor, type $II_{1}$      148 305
Factor, type $II_{\infty}$      148 150 305
Factor, type $I_{n}$      148
Factor, type I      148 355 356
Factor, type II      148 150
Factor, type III      134 148 149 150 151 421 464
Fell      459
Feller      303
Field, relativistic      3 461
Fock      8
Form, bilinear      93 94 102
Form, sesquilinear      214 270
Fourier analysis      25 94 241 243 244
Fourier analysis transform(ation)      244 250 253 257 260 417
Friederichs      9
Friederichs extension      104
Fujii, Furuta, and Matsumoto      313
Fukamuja      152
Fukamuja Misonou, and Takeda      460
Full family of states      220 221 222 305
Function analytic      91
Function of positive type      463
Function, affine      66 319 321 325 327 330 336—339 349 364
Function, almost periodic      400 401 430 435 436 464
Function, Borel      5
Function, concave      326 328 336
Function, convex      321 325 326 327 331 332 333 353 355 377
Function, countably additive set      321
Function, lower semi-continuous      377
Function, subadditive      65 329 336 337
Function, superadditive      336 337
Function, trignometric      430
1 2 3
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