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

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Название: Theory of Operator Algebras III

Автор: Takesaki M.

Аннотация:

Together with "Theory of Operator Algebras I, II", this book, written by one of the most prominent researchers in the field of operator algebras, summarises the scientific work of the author focusing on von Neumann algebras and non-commutative integration. The book is part of the recently developed part of the "Encyclopaedia of Mathematical Sciences" on operator algebras and non-commutative geometry. The book provides essential and comprehensive information to 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: 548

Добавлена в каталог: 16.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(n, \lambda)$-array      302
$(n, \lambda_1, \lambda_2)$-array      398
$\delta$-related      227
$\lambda$-Markov trace      433
$\omega$-asymptotic centralizer      379
Absolutely free action      12
Abstract operator space      168
Action of a locally compact group, absolutely free      12
Action of a locally compact group, characteristic invariant of an ~      411
Action of a locally compact group, ergodic      4
Action of a locally compact group, free      4
Action of a measured groupoid      53
Action of a measured groupoid, ancillary      53
Action of a measured groupoid, localization      59
Admissible submatrix unit      210
AF-algebra      84 412—413
AF-groupoid      36
AFD factor      81
AFD factor, locally      see LAFD factor
Algebra, CAR      92
Algebra, Fermi      92
Algebra, Fermion      92
Algebra, Jones — Temperley — Lieb      459
Almost connected group      64
Almost connected group $\alpha$-cocycle      59
Amenability, strong      493
Amenable group      62
Amenable groupoid      70
Analytic vector      499
Ancillary action      53
Ancillary groupoid      53
Aperiodic automorphism      255
Approximable completely positive map      168
Approximately finite dimensional algebra      see AF-algebra
Approximately finite dimensional factor      see AFD factor
Approximately finite dimensional von Neumann algebra      97
Approximately finite groupoid      see AF-groupoid
Approximation, completely positive      154
Array      39
Array, $(n, \lambda)-\sim$      302
Array, $(n, \lambda_1, \lambda_2)-\sim$      398
Associated flow      30
Asymptotic Bicentralizer      329
Asymptotic Centralization      329
Asymptotic centralizer      329
Asymptotic outer period of an automorphism      261
Asymptotic ratio set      23
Atom of an array      43
Automorphism, aperiodic      255
Automorphism, approximately inner      270 371
Automorphism, approximately inner, locally      371
Automorphism, centrally trivial      126 261
Automorphism, liftable      133
Automorphism, outer conjugate      267
Automorphism, outer period of an ~      261
Automorphism, outer period of an, asymptotic      261
Automorphism, periodic      255
Automorphism, properly outer      253
Automorphism, semi-liftable      133
Banach spaces, pair of compatible ~      509
Basic construction      443
Basic tower construction of Jones      426 443
Basis, standard      444
Bicentralizer, asymptotic      329
Bilinear form, unital bounded      187
Bimodule, finite      438
Body of a tree      518
Borel function      20
Bounded bilinear form, unital      187
Bounded finite Type I, subgroupoid of      38
Bounded sequence, $\omega$-central      116
Bounded sequence, strongly $\omega$-central      116
Bounded sequence, trivial $\omega$-central      116
Bounded subset      71
Bounded vector      439
Branch of a tree      519
Bratteli diagram      414
Bratteli — Pascal diagram, half      460 464^65
Bratteli — Pascal diagram, truncated      441 457 459
C*-algebra of type I      156
C*-algebra, conjugate      82
C*-algebra, inductive sequence of ~s      82
C*-algebra, nuclear      153 156
C*-algebra, proper      83
C*-algebra, unital      82
Canonical anti-commutation relation (CAR)      91
Canonical isomorphism      414
CAR algebra      92
Central sequence      108
Central sequence, $\omega$-hypercentral      117
Central sequence, equivalent strongly ~s      116
Central sequence, equivalent ~s      116
Central sequence, hypercentral      117
Central sequence, strongly      108
Central sequence, strongly trivial      108
Centralization, asymptotic      329
Centralizer, $\omega$-asymptotic      379
Centralizer, asymptotic      329
Centralizing sequence      108
Centrally trivial automorphism      126
Characteristic Group      128
Characteristic invariant      295
Characteristic invariant of an action      411
Co-Souslin set      516
Coanalytic set      516
Coboundary      54
Coboundary function      25
Cocycle      59
Cocycle conjugate      53
Cocycle identity      25
Cocycle, one      25
Cocycle, two      54
Cohomologous element      59
Cohomology group, first      25
Cohomology reduction theorem      48 56 79 322 326 397
Cohomology vanishing theorem      55 316
Commuting square      467
Compatible Banach spaces      509
Complete contraction      167
Complete isometry      167
Completely bounded map      167
Completely positive approximation      154
Completely positive contraction      156—157 160—161 166
Completely positive lifting      168
Completely positive map      174
Completely positive map, approximable      168
Completely positive map, liftable      168
Complex interpolation norm      510
Complex interpolation space      510
Concrete operator space      168
Conjugate, cocycle      53
Contraction, completely positive      156—157 160—161 166
Convergence, strong resolvent      500
Convex approximate identity      169
Core      498 506
CP-map      see Completely positive map 0
Cross homomorphism      54
Depth      469
Depth, finite      469
Depth, infinite      469
Diagonal element      43
Dimension group      415 417
Dimension group, scaled      414
Dimension vector      442
Dimension, relative      420
Domain      504
Dual inclusion      466
Dual principal graph      469
Dyadic adding machine      47
Dyadic group      37
Dyadic group, completely      37
Dyadic groupoid      37
Dyadic odometer transformation      47
Eigenvalue, Frobenius — Perron      481
Eigenvalue, Perron — Frobenius      515
Eigenvector, Frobenius — Perron      481
Eigenvector, Perron — Frobenius      515
Element, cohomologous      59
Element, diagonal      43
Element, hermitian      513
Equivalence class, unitary, of an isomorphism      413
Equivalence of $\omega$-central sequences      116
Equivalence of homomorphisms      33
Equivalence of sequences      108
Equivalence relation, reduced      23
Equivalence, orbit      24
Ergodic action      4
Ergodic measure      31
Ergodic transformation group      1
Essentially self-adjoint      499
Even state      94
Exact sequence      328
Exact sequence, short      54 308
Extension of a subgroupoid      77
Extension of a von Neumann algebra by a von Neumann subalgebra      442
Factor of type $\mathrm{III}_\lambda$      23
Factor of type $\mathrm{II}_1$      7 22—23 95 97
Factor of type $\mathrm{II}_1$, locally aproximately finite dimensional (LAFD)      249
Factor of type $\mathrm{II}_\infty$      7 22—23
Factor of type I      7 22
Factor of type III      22
Factor of type III, strongly $\lambda$-stable      370
Factor, stable      115
Factor, strongly stable      115
Fast reindexing      134
Fermi algebra      92
Fermion algebra      92
Finite depth      469
Finite index (of a tunnel)      486
First cohomology group      25
Flow of weights, associated      30
Flow of weights, non-commutative      28
Fock representation      93
Fock vacuum vector      93
Folner's condition      68
Form sum      507
Form, quadratic      see Quadratic form
Free action      4
Free ultra filter      116
Frobenius — Perron eigenvalue      481
Frobenius — Perron eigenvector      481
Full factor      112
Full group      24
Full von Neumann algebra      108
Function, Borel      20
Function, coboundary      25
Function, left uniformly continuous      60
Function, right uniformly continuous      60
Function, Steinhaus      198
Functional, unital      511
Functional, unital bounded linear      194
Generating tunnel      477
Generating tunnel of Jones      477
Generator, infinitesimal      498
Global index      421
Graph, dual principal      469
Graph, principal      469
Grothendieck — Haagerup — Pisier inequality      186
Group C*-algebra, reduced      66
Group measure space construction      1
Group, almost connected      64
Group, amenable      62
Group, characteristic      128
Group, completely dyadic      37
Group, dyadic      37
Group, full      24
Group, one parameter unitary      497
Group, Polish      109
Group, scaled dimension      414
Groupoid      31
Groupoid of type $\mathrm{II}_1$      36
Groupoid of type $\mathrm{II}_\infty$      36
Groupoid of type $\mathrm{I}_k$      36
Groupoid of type $\mathrm{I}_\infty$      38
Groupoid of type I      36 38
Groupoid of type III      36
Groupoid, action of a measured ~      53
Groupoid, ancillary      53
Groupoid, approximately finite      see AF-groupoid
Groupoid, associated measured      56 59 70
Groupoid, derived      33
Groupoid, dyadic      37
Groupoid, measurable      34
Groupoid, measured (principal)      35
Groupoid, measured, ergodic      36
Groupoid, multipliable pairs in a ~      31
Groupoid, orbitally countable      34
Groupoid, orbitally discrete      34
Groupoid, orbitally finite      34
Groupoid, principal      33
Groupoid, reduced      33
Groupoid, semi-direct product      58
Groupoid, similar      33
Hermitian element      195 513
Higher relative commutants      466
Homomorphism of a sequence      82
Homomorphism of groupoids      33
Homomorphism, cross      54
Homomorphism, equivalent      33
Homomorphism, similar      33
Hypertrace      179
Identity, convex approximate      169
Inclusion matrix      442
Inclusion, dual      466
Index of a conditional expectation      440
Index of a subfactor      412 421—422
Index of a subfactor, global      421
Index of a subfactor, local      422
Index Selection      135
Index, finite, of a tunnel      486
Inductive limit      82—83
Inductive sequence of C*-algebras      82
Inductive sequence of C*-algebras, conjugate      82
Inductive sequence of C*-algebras, proper      83
Inductive sequence of C*-algebras, unital      82
Inequality of Grothendieck — Haagerup — Pisier      186
Infinite depth      469
Infinite tensor product      84—85
Infinitesimal generator      498
Initial segment      516
Injective von Neumann algebra      155
Intrinsic invariant      292
Invariant mean, left      62 70
Invariant, characteristic, of an action      295 411
Invariant, intrinsic      292
Invariant, modular      311 408
Inverse      32
Irreducible subfactor      493
Isometry, complete      167
Isomorphism, canonical      414
Isomorphism, equivalence class of an ~      413
Isomorphism, fast reindexing      134
Isomorphism, slow reindexing      134
Jones polynomial      493
Jones tower      443
Jones — Temperley — Lieb algebra      459
Jones — Temperley — Lieb relation      459
Jones' basic construction      443
Jones' basic tower construction      426
Jones' tunnel      475
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