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Takesaki M. — Theory of Operator Algebras II
Takesaki M. — Theory of Operator Algebras II

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Название: Theory of Operator Algebras II

Автор: Takesaki M.

Аннотация:

The book provides essential and comprehensive information for graduate students and researchers in mathematics and mathematical physics.


Язык: en

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 518

Добавлена в каталог: 16.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L^1$-bundle algebra      441
$\alpha$-cocycle      240
$\alpha$-integrable      265
$\alpha$-one cocycle      240
$\alpha$-representation      333
$\alpha$-spectrum      313
$\alpha$-twisted *-representation      266
$\mathcal M, \tau$-measure topology      167
$\mathcal M-\mathcal N$-bimodule      186
$\mathcal M-\mathcal N$-bimodule, conjugate      186
$\mathcal M-\mathcal N$-bimoduledual      186
$\mathcal N$-module, faithful      186
$\mathcal N$-module, right      186
$\sigma$-topology      315
$\tau$-dense subspace      183
$\tau$-measurable operator      173
$\tau$-measurable operator algebra      174
$\tau$-measurable operator algebra, abstract      174
$\tau$-measurable operator algebra, concrete      174
$\tau$-measure convergence      167
$\tau$-measure topology      167
$\tau$-nearly everywhere convergence      183
*-derivation      352
*-representation, anti      3
Absolute value      161 174
Action of a locally compact group      238
Action of a locally compact group, dominant      270
Action of a locally compact group, dual      260 278 309
Action of a locally compact group, free      346
Action of a locally compact group, reduced      332
Action of a locally compact group, regular      336
Additive coboundary      344
Additive one cocycle      344
Ambrose — Kakutani — Kubo — Krengel theorem      363 385
Amenable group      309
Analytic vector      467
Anti-representation      186 190 205
Arveson Spectrum      313
Associated covariant system      368
Associated system, discrete      383
Automorphism group, modular      see Modular ~
Automorphism group, one parameter      see One parameter ~
Automorphism, extended inner      453
Automorphism, extended modular      376
Automorphism, free      346
Automorphism, induced      395
Automorphism, scaling      368
Balanced Weight      107
Banach spaces, pair of compatible      477
Bimodule      186
Bimodule, conjugate      186
Bimodule, dual      186
Bimodule, full      186
Bimodule, standard      186
Body of a tree      486
Bounded Vector, left      9
Bounded Vector, right      5
Branch of a tree      487
C*-covariant system      279 333
C*-crossed product, reduced      309
Canonical core      446
centralizer      91 98 127
Centrally ergodic covariant system      288
Centrally ergodic disintegration      289
Chain rule      115
Character (of a dual group)      77
Characteristic square      453 455
Co-Souslin set      484
Coanalytic set      484
Coboundary (additive)      344
Cocycle conjugate      240
Cocycle derivation theorem      111
Cocycle derivative      111 127 232
Cocycle, $\alpha$-one-~      240
Cocycle, $\alpha$-~      240
Cocycle, additive one      344
Cocycle, dominant      270
Cocycle, equivalent ~ s      240
Cocycle, H-valued one      389
Cohomology class      455
Cohomology group, first      376
Cohomology group, second      277
Cohomology space, one      240
Cohomology vanishing theorem      311 357
Coisometry      418
Commutation relation of Heisenberg — Weyl      257
Commuting elements      98
Compatible Banach spaces      477
Complex interpolation norm      478
Complex interpolation space      478
Conditional expectation      211
Cone, dual      143
Cone, extended positive      215
Cone, self-dual      143
Conjugate bimodule      186
Conjugate covariant systems      240
Conjugate, cocycle      240
Conjugation, modular      151
Connes spectrum      332
Continuous decomposition      368
Convergence, $\tau$-nearly everywhere      183
Convergence, strong resolvent      468
Core      466 474
Core, canonical      446
Core, discrete      383
Correspondence      236
Covariant representation      240 257
Covariant system      238
Covariant system, associated      368
Covariant system, C*-~      279 333
Covariant system, centrally ergodic      288
Covariant system, conjugate      240
Covariant system, discrete associated      397
Covariant system, dual      260
Covariant system, ergodic      288
Covariant system, free      271
Covariant system, homogeneous      330
Covariant system, induced      301
Covariant system, reduced      332
Covariant system, stable      271
Crossed product      241
Crossed product, full      309
Crossed product, reduced C*-~      309
Decomposition      289
Decomposition, continuous      368
Decomposition, discrete      383
Definition domain      42
Definition subalgebra      42
Derivation      352
Derivation, *-~      352
Derivation, inner      352 358
Derivative, cocycle      see Cocycle derivative
Derivative, spacial      191
Diameter      430
Direct integral      30 135
Direct integral of Hilbert algebras      32
Direct integral of Tomita algebras      33
Direct integral, Tomita algebra      33
Discrete associated covariant system      397
Discrete associated system      383
Discrete core      383
Discrete decomposition      383
Disintegration, centrally ergodic      289
Disintegration, equivariant      279 282
Disintegration, ergodic      289
Disintegration, existence of      35
Disjoint elements      267
Divisible by      2 277
Domain      472
Domain, definition      42
Dominant action      270
Dominant cocycle      270
Dominant weight      418
Dual action      260 278 309
Dual bimodule      186
Dual cone      143
Dual covariant system      260
Dual group      77
Dual group, character of a      77
Dual weight      249
Eigenvalue, Perron — Frobenius      483
Eigenvector, Perron — Frobenius      483
Element, entire      98
Element, faithful      216
Element, hermitian      481
Element, of exponential type      128
Element, semi-finite      216
Entire element      98
EQUIVALENCE      267
Equivalence of cocycles      240
Equivalence of left Hilbert algebras      10
Equivalence of weights      403
Equivalence, quasi      267
Equivariant disintegration      279 282
Ergodic covariant system      288
Ergodic covariant system, centrally      288
Ergodic disintegration      289
Ergodic flow, properly      385
Essential spectrum      332
Essentially self-adjoint      467
Exact sequence      277 451 453
Exact sequence, short      376
Existence of disintegration      35
Expectation, conditional      211
Exponential type      128
Extended inner automorphism      453
Extended modular automorphism      376
Extended positive cone      215
Extended unitary group      449
Eymard — Steinespring — Tatsuuma duality theorem      90
Factor      142
Factor of type $\mathrm{III}_0$      363 369 384
Factor of type $\mathrm{III}_1$      363 369
Factor of type $\mathrm{III}_\lambda$      363 368
Factor of type $\mathrm{II}_1$      65 290
Factor of type $\mathrm{II}_\infty$      364 380 384
Faithful element      216
Family of orderings, one parameter      421
Field, measurable      see Measurable field
First cohomology group      376
Flow of weights      363 368
Flow of weights, built under a ceiling function      385
Flow of weights, global      407
Flow of weights, non-commutative      364 368 437 449
Flow of weights, properly ergodic      385
Flow of weights, smooth      419
Form sum      218 475
Form, quadratic      see Quadratic form
Form, standard      see Standard form
Fourier algebra      69
Fourier transform      74
Fourier-Stieltjes algebra      84
Free action      346
Free automorphism      346
Full bimodule      186
Full crossed product      309
Function, positive definite      79
Function, two-point      95
Functional, unital      479
Fundamental set of vector fields      28
Gelfand transform      74
Generalized trace      383
Generator, analytic      128
Generator, infinitesimal      325 466
Generator, logarithmic      128
Generator, multiplicative      128
Global flow of weights      407
Grade      457
Graph norm      26 28
Group C*-algebra, reduced      78
Group von Neumann algebra, left      65
Group von Neumann algebra, right      65
Group, divisible by      2 277
Group, dual      77
Group, extended unitary      449
Group, one parameter unitary      465
Group, unitary      449
H-valued one cocycle      389
Heisenberg — Weyl commutation relation      257
Hereditary subset      52
Hermitian element      481
Hilbert algebra      2
Hilbert algebra, equivalent      10
Hilbert algebra, full left      10
Hilbert algebra, left      2
Hilbert algebra, right      2
Hilbert algebra, unimodular      2
Hilbert space in a von Neumann algebra      348
Hille — Yosida theorem      326
Hitting number      387
Hitting time      387
Hitting time, n-th      387 395
Homogeneous covariant system      330
Implementation, standard      153
Imprimitivity system      296
Induced automorphism      395
Induced covariant system      301
Induced representation      295
Infinite multiplicity      268
Infinite multiplicity of a weight      398 405
Infinitesimal generator      325 466
Initial segment      484
Inner derivation      352 358
Integrable      265 418
Integrable, $\alpha$-~      265
Integrable, square      185 266
Intrinsic invariant      455
Invariant, intrinsic      455
Joint spectrum      157
KMS-condition      92 140
Krieger's hierarchy tower      403
Kubo — Martin — Schwinger boundary condition      92
Lacunary weight      397
Left Hilbert algebra      2
Length      484
Lie — Trotter formula      164
Measurable field, of Hilbert spaces      30
Measurable field, of left Hilbert algebras      28
Measurable field, of normal weights      134
Measurable field, of right Hilbert algebras      28
Measurable field, of Tomita algebras      33
Measurable field, uniqueness of ~ s      36
Measurable operator      173
Measure topology      167
Modular automorphism group      22 95 127 232
Modular condition      91—92
Modular conjugation      5 151
Modular operator      5
Modular period group      369
Modular spectrum      369
Module      186
Module, faithful right      186
Module, right      186
Modulus      368 419
Modulus, quantized      449
Multiplicity      257
Multiplicity, infinite      268
Multiplicity, infinite, of a weight      398 405
n-th hitting time      387 395
Norm, graph      26 28
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