Takesaki M. — Theory of Operator Algebras III :: Электронная библиотека попечительского совета мехмата МГУ

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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:

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

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Предметный указатель

Jones' tunnel, generating      477
Krieger's construction      15
LAFD factor      249
Left invariant mean      62 70
Left uniformly continuous function      60
Length      516
Liftable automorphism      133
Liftable completely positive map      168
Lifting      168
Lifting, completely positive      168
Limit, inductive      83
Local index      422
localization      59
Locally approximately inner automorphism      371
Locally aproximately finite dimensional factor      see LAFD factor
Map, complete contraction      167
Map, completely bounded      167
Map, completely posivite      see Completely positive map
Map, unital      165
Markov trace      433
Markov trace of modulus t      446
Maximal abelian action      4
Maximal abelian subalgebra      137
Maximal abelian subalgebra, regular      137
Maximal abelian subalgebra, semi-regular      137
Maximal abelian subalgebra, singular      149
Measurable groupoid      34
Measurable groupoid, orbitally countable      34
Measurable groupoid, orbitally discrete      34
Measurable groupoid, orbitally finite      34
Measure, $\sigma$ -finite, quasi-invariant      35
Measure, ergodic      31
Measured principal groupoid      35
Measured principal groupoid, ergodic      36
Modular invariant      311 408
Modular obstruction      311 329 408
Modulus      16 35
Multimatrix algebra      413
Multipliable pairs, set of      31
Non-commutative flow of weights      28
normalizer      24—25 137
Nuclear C*-algebra      153
Numerical range      511
Obstruction      284
Obstruction, modular      311 329 408
Odometer transformation      317
Odometer transformation, dyadic      47
One cocycle      25
One parameter unitary group      497
Operator space, abstract      168
Operator space, concrete      168
Orbit      34
Orbit equivalence      24
Orbitally countable      34
Orbitally discrete      34
Orbitally finite      34
Order      39
Orthogonal submatrix units      210
Outer conjugate automorphisms      267
Outer period of an automorphism      261
Partial transformation      16
Partial transformation, belonging to a subgroupoid      38
Pascal triangle      417
Period, asymptotic outer, of an automorphism      261
Period, outer, of an automorphism      261
Periodic automorphism      255
Perron — Frobenius eigenvalue      515
Perron — Frobenius eigenvector      515
Polish group      109
Principal graph      469
Principal graph, dual      469
Principal groupoid      33
Principal groupoid, ergodic      36
Principal groupoid, measured      35
PRODUCT      32
Product state      94
Product, groupoid, semi-direct      58
Product, semi-direct      58
Proper inductive sequence of C*-algebras      83
Properly outer automorphism      253
Property $\Gamma$       410
Quadratic form      504
Quadratic form, closable      506
Quadratic form, closed      506
Quotient Borel structure      31
Radical of a group      64
RANGE      32
Reduced equivalence relation      23
Reduced group C*-algebra      66
Refinement of a submatrix unit      210
Refinement of an array      39^0
Regular von Neumann subalgebra      137
Reindexing, fast      134
Reindexing, slow      134
Relation, Jones — Temperley — Lieb ~      459
Relative dimension      420
Representation of the canonical anti-commutation relation      91
Representation, Fock ~      93
Right uniformly continuous function      60
Rokhlin tower      255
Rokhlin's theorem      44 252 255
Saturation      34
Scaled dimension group      414
Section      37

Self-adjoint, essentially      499
Semi-direct product      58
Semi-direct product groupoid      58
Semi-discrete von Neumann algebra      178
Semi-liftable automorphism      133
Semi-regular von Neumann subalgebra      137
Separability      97
Sequence, $\omega$ -central      116
Sequence, bounded      see Bounded sequence
Sequence, central      see Central sequence
Sequence, centralizing      108
Sequence, equivalence of ~s      108
Sequence, exact      328
Sequence, short exact      54 308
Sequence, strongly $\omega$ -central      116
Sequence, trivial $\omega$ -central      116
Set of multipliable pairs      31
Set, co-Souslin      516
Set, coanalytic      516
Similarity of groupoids      33
Similarity of homomorphisms      33
Slow reindexing      134
Source      32
Souslin set      516
Stabilizer      6
Stable factor      115
Standard basis      444
State, even      94
State, product      94
Steinhaus functions      198
Strong amenability      493
Strong resolvent convergence      500
Strongly $\lambda$ -stable factor      370
Strongly $\omega$ -central sequence      116
Strongly central sequence      108
Strongly central sequence, trivial      108
Strongly stable factor      115
Subalgebra, maximal abelian      see Maximal abelian subalgebra
subarray      40
Subfactor, irreducible      493
Subgroupoid of bounded finite type      138
Subgroupoid, extension of a ~      77
Submatrix unit      209
Submatrix unit, admissible      210
Submatrix unit, orthogonal      210
Subset belonging to a $\sigma$ -field      43
Subset, bounded      71
Subspace, unital      155
Support of a submatrix unit      241
Support of a von Neumann algebra      39
Tensor product, infinite      84—85
Tower      443
Tower of the higher relative commutants      466
Trace      418
Trace, Markov, $\lambda$ -Markov      433
Trace, Markov, $\lambda$ -Markov, of modulus t      446
Transformation, belonging to a subgroupoid      38
Transformation, partial      16
TREE      516
Tree, body of a ~      518
Tree, branch of a ~      519
Tree, finitely terminated      516
Tunnel of finite index      486
Tunnel, generating      477
Tunnel, generating, of Jones      477
Two cocycle      54
Type $\mathrm{III}_\lambda$ factor      23
Type $\mathrm{II}_1$ factor      7 22—23
Type $\mathrm{II}_1$ factor, uniqueness      95 97
Type $\mathrm{II}_1$ groupoid      36
Type $\mathrm{II}_\infty$ factor      7 22—23
Type $\mathrm{II}_\infty$ groupoid      36
Type $\mathrm{I}_k$ groupoid      36
Type $\mathrm{I}_\infty$ groupoid      38
Type I C*-algebra      156
Type I factor      7 22
Type I groupoid      36
Type I groupoid, bounded finite      38
Type III factor      22
Type III groupoid      36
Ultra filter, free      116
Ultra product technique      115
Uniformly continuous function (left, right)      60
UNIT      32
Unital bounded bilinear form      187
Unital bounded linear functional      194
Unital inductive sequence of C*-algebras      82
Unital map      165
Unital subspace      155
Unitary group, one parameter      497
Vector, abounded      439
Vector, analytic      499
Vector, weight      442
von Neumann algebra      see Neumann algebra
von Neumann algebra, approximately finite dimensional (AFD)      97
von Neumann algebra, associated      4 15
von Neumann algebra, diffused abelian      79
von Neumann algebra, discrete      178
von Neumann algebra, full      108
von Neumann algebra, injective      155
von Neumann algebra, semi-discrete      178
von Neumann subalgebra, maximal abelian, regular      137
von Neumann subalgebra, maximal abelian, semi-regular      137
Weight vector      442
Weight, centralizer of a ~      329 379

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