Bratteli O., Robinson D.W. — Operator Algebras and Quantum Statistical Mechanics (vol. 1) :: Электронная библиотека попечительского совета мехмата МГУ

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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.

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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

Предметный указатель

Representations, direct sum of      81
Representations, disjoint      370
Representations, equivalent      48 370
Representations, inequivalent      9
Representations, measurable family of      447
Representative      43
Resolvent      25 27 91 165 168 169 170 184 274 306 311
Resolvent convergence      184 186 188
Rickart      305
Rieffel      155
Riemann approximant (sum)      167 243
Riemann approximant (sum), integral      33 215 243
Riesz and Nagy      152 304
Roberts      304
Robertson      305
Robinson      304—307
Root mean square deviation      349
Rudin      152
Ruelle      9
Russo and Dye      305
Sakai      76 152 155 306 307 309 311 312 459 460
Saturation problem      304
Sch winger      13
Schrodinger      3 6
Schrodinger equation      4
Schultz      8
Schur's lemma      153
Schwartz      152
Schwartz reflection principle      275
Sector of an operator      292
Segal      7 8 9 16 152 153 461
Semigroup      161 164 165 166 167 168 203
Semigroup, $C_{0}$ -      164 169—178 187—194 202 235 304
Semigroup, $C_{0}^{*}$ -      164 170 171 183 193—196 202 205 303 304
Semigroup, dual      303
Semigroups, convergence of      184—192
Seminorm      65 66 163 168 174
Seminorm, $\tau(X,F)$ -      204
Seminorm, C*-      138
Separability condition S,      352 353 367 372 377 378 426 427 428 432 436 440 447 449 450 454 455 460
Separating subset      85
Separating vector      80 86 88 109 226—230 277—289 311—444
Set metrizable      132 133 318 331 333 339 458
Set, $F_{\sigma}$ -      322 357 372 373
Set, $G_{\delta}$ -      322 331 332 333 338 357 458
Set, $\mu$ -measurable      356 357 452 454
Set, $\mu$ -negligible      356 357 440
Set, analytic      295 357 458 460
Set, Baire      see "Baire set"
Set, Borel      see "Borel set"
Set, convex      53 59 66 317—359
Set, directed      39 46 121 123 324 331 345
Set, pseudo supporting      322 331
Set, resolvent      25
Set, stable      331 342
Set, supporting      322 357 426
Sherman      460
Simon      152 304
simplex      334 335 367 368 385 386 387 405 406 458 464
Simplex, Bauer      464
Simplex, Poulsen      464
Skau      458 460
Sommerfeld      3
Space analytic Borel      295
Space configuration      120
Space quotient      23
Space, conjugate      70
Space, direct integral      439—442 449
Space, direct sum      439
Space, measurable family of      441 442 444 447 449
Space, Polish      295 440 456
Spectral concentration      253
Spectral projector (projection)      58 71 87 104 132 135
Spectral radius      25 26 29 31 37 44 59 241 312
Spectral subspace      251 252 257 259 410
Spectral theory      7 249 281 298 308
Spectral values      252
Spectrum      25 26 28 32 35 51 61 62 142 149 165 220 240 245 248 251 252 256 257 263 294 306 309 407 419 420 434 464
Spectrum of an abelian C*-algebra      61
Spectrum point      407 412—415 419—421 424 436 455 457 464
Spectrum, $\Gamma$       310
Spectrum, Arveson      310
Spectrum, semi-bounded      261
Spin system      311
Square root      32 34 36 152 235 236 306
Stability      13 160 184 202
Standard form      83 155 226 228 305
State      42 48 51 153 344 345 346 350 352 353 358 361 363 439 452
State equilibrium      11 12 268
State factor      81 128 317 356 358 372 401 402 403 452 460
State, (G-) ergodic      374 377 378 393—398 401 405 407 408 410 413 418 420 423 424 428 440 452 459—464
State, (G-) invariant      13 117 240 268 272 311 374—387 390 393 398 400 402—407 414 415 423 427 431 432 434 459 461 462
State, almost periodic      414 424 430—433
State, centrally ergodic      395 396
State, extremal G-invariant      318
State, faithful      13 83 85 96 299 403
State, ground      9 273 277 289 309
State, KMS-      285
State, locally normal      118 124 125 129 133 219 317 352 356 373 460
State, mixed      6
State, normal      7 9 75 76 78 79 80 83 96 129 131 210 219 220 238 299 355 370 371 383 390 398 452 460 462
State, periodic      414
State, physical      7 122
State, primary      81
State, pure      6 53 57 58 62 153 343 350 351 352 356 358 359 367 368 372 405 452 461
State, regular      8 9
State, trace      84
State, vector      49 131 356 395
States, disjoint      9 370 395
States, neighbouring      219
States, orthogonal      339 340
States, set of      7 53 59 61
Statistics, Bose      121
Statistics, Fermi      121 156
Sternfeld      464
Stinespring      305
Stone      5 16
Stone-von Neumann uniqueness theorem      6 8 9
Stormer      8 16 305 462 464

Subalgebra      19
Subalgebra, central      124
Subalgebra, fixed point      137 149
Subspace, cyclic      46
Subspace, invariant      44
Subspace, measurable      441
Subspace, stable      44
Summable central sequence      309
Support of a measure      318 322 376 377 427 432 435 436 437 453
Support, finite      322—330 335 337 361 363 371 377 432
Symmetry      136 209 374 423 424
Symmetry, broken      374 413 423
Symmetry, Wigner      210 225 226 248 305 307
Takeda      460
Takesaki      13 83 155 310
Takesaki and Tomiyama      459
Taylor series      34
Tensor product      142 143 144 145
Theorem capacity      460
Theorem monotone convergence      327
Theorem uniform boundedness      100
Theorem, Alaoglu      98
Theorem, Alaoglu — Bourbaki      53 68 154 163 168 176 205
Theorem, bicommutant      72 445
Theorem, Bochner      103
Theorem, Borchers — Arveson      261 263 269 309 421
Theorem, Caretheodory — Minkowski      321
Theorem, Carlson's      91 155
Theorem, Cartier — Fell — Meyer      460
Theorem, closed graph      207 235
Theorem, Connes — Takesaki duality      149
Theorem, Connes' Radon — Nikodym      147
Theorem, derivation      262
Theorem, Effros'      450
Theorem, Fubini's      257 258
Theorem, Hahn — Banach      59 60 61 65 66 75 101 154 174 200 218 221 325 328 329 339 360 403
Theorem, Hille — Yosida      171 173 174 178 181
Theorem, Kadison's (transitivity)      154 402
Theorem, Kaplansky density      74 103 122 123 154 218 232 236 347
Theorem, Kovacs — Szucs mean ergodic      383
Theorem, Krein — Milman      53 59 61 153 217
Theorem, Krein — Smulian      98 155 341
Theorem, Lebesgue dominated convergence      100 185 186 412 428 437
Theorem, Liouville's      275
Theorem, Lumer — Phillips      177
Theorem, Mackey — Arens      223
Theorem, Mackey's      98
Theorem, Markov — Kakutani fixed point      415
Theorem, Mazur's      403 464
Theorem, mean ergodic      378 383 386 391 394 398—400 411 415 421 422 462
Theorem, Pontryagin's duality      139
Theorem, Radon — Nikodym      213
Theorem, Riesz representation      68 70 83 213 239 322 350
Theorem, Sakai's      76
Theorem, SNAG (Stone — Naimark — Ambrose — Godement)      250
Theorem, Spectral      5
Theorem, Spectral Mapping      31
Theorem, Stone — von Neumann uniqueness      6
Theorem, Stone — Weierstrass      24 63 64 325 346 347 376 387
Theorem, Stone's      251
Theorem, Tauberian      250 253
Theorem, Tomita — Takesaki      94 155 311
Theorem, Tomita's      341 450 452
Theorem, Trotter — Kato      304
Theorem, von Neumann density      72 73 74 154
Thermodynamic limit      10
Time development      160
Tomita      13 83 459 460
Tomita — Takesaki theory      13 83 84 91 146
Tomiyama      459
Tomiyama, property Ј of      150
Topology quotient      295
Topology uniform (norm)      20 25 53 70 108 127 131 163 169 194 289 355
Topology, $\sigma$ -strong      66 70 74
Topology, $\sigma$ -strong*      69 70 74
Topology, $\sigma$ -weak      67 70 74 78 279 445
Topology, $\sigma(X,F)$ -      97 98 99 163 166 171
Topology, discrete      435
Topology, locally convex      59 65 97 163
Topology, locally uniform      132 133
Topology, Mackey ( $\tau(X,F)$ -)      98 155 163 164 167 169 174 184
Topology, metric      20 132 133
Topology, strong      66 69 70 74 108 295
Topology, strong operator      127 309
Topology, strong*      69 70 74 108 295
Topology, weak      67 70 74 108 295 356
Topology, weak operator      3 341
Topology, weak* ( $\sigma(\mathfrak{A}^{*},\mathfrak{A})$ -)      14 53 68 131 132 176 181 206 317 329 335 337 346 355 377 406
Trace      145 280 281 287
Trace norm      68
Trace, faithful      148 149
Trace, normal      148 149
Trace, semifinite      148 149
Translations, space      13
Trotter      304
Trotter product formula      304
Twist      206 302
Urysohn's lemma      332
van Daele      155
Van der Waerden      16
Vaught      152
Vector, almost periodic      408
Vector, cyclic      see "cyclic vector"
Vector, separating      see "separating vector"
von Neumann      3 5 11 16 154 465
Weight      145 146
Weight, dual      311
Weight, faithful      146 147 149
Weight, normal      146 147 149
Weight, semifinite      146 147 148 149
Weyl      6
Weyl, criterion      253
Wightman      9 16 463
Wigner      7 see Wigner"
Wils      460
Winnink      13
Woronowicz      155 312
Yngvason      463
Yosida      152 303 464
Zorn's lemma      46 77 326 332 441 458

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