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

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Takesaki M. — Theory of Operator Algebras I

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Название: Theory of Operator Algebras I

Автор: Takesaki M.

Аннотация:

The unifying theme is the Banach space duality for operator algebras, allowing readers to recognize the affinity between operator algebras and measure theory on locally compact spaces.

Язык:

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2001

Количество страниц: 415

Добавлена в каталог: 16.04.2005

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Предметный указатель

$C(\infty)$ -direct sums      157
group algebra of G      6
$\alpha$ -homogeneous central projections      299
$\mathcal A$ -valued trace      298
$\mathcal L(\matfrak{h})$ -valued measurable functions      258
$\mu$ -measurable E-valued functions      253
$\sigma$ -finite von Neumann algebras      78
$\sigma$ -strong (operator) topology      68
$\sigma$ -strong* (operator) topology      68
$\sigma$ -weak (operator) topology      67
(Left) group von Neumann algebra of G      364
*-algebra of operators on $\mathfrak{h}$       72
*-algebra of operators on $\mathfrak{h}$ , nondegenerate      72
*-homomorphisms      21
*-operation      2
A*-algebras      42
Abelian Banach algebras      13—16
Abelian projections      296
Absolute value of $\varphi$       142
Absolute value of h      20
Absolute value of x      24
Absolutely continuous spectrum      66
Absolutely invariant projections      363
Action of a group      363
Action of a group, ergodic      363
Action of G on A      46
Adjoint cross-norm      190
Adjoint functional off      36
Affine functions      158
Amplification isomorphism      184
Approximate identity of A      26
Arens — Mackey topology      153
Asymmetric Riesz decomposition theorem      29
Atomic representations      176
Atomic representations, universal atomic representation      176
Atomic von Neumann algebras      155
B*-algebra      55
Banach algebras      2
Banach algebras, abelian      13—16
Banach algebras, involutive      2
Banach algebras, semisimple      16
Banach algebras, unital      3
Barycenter of $\mu$       233
Borel spaces      375
Boundary measures      235
Boundary set off      234
C*-algebra of operators      72
C*-algebras      2
C*-algebras, dual      157
C*-algebras, monotone closed      137
C*-algebras, primitive      178
C*-algebras, weakly compact      157
C*-homomorphisms      188
C*-subalgebra of A generated by E      18
C*-subalgebras      18
C*-subalgebras, unital      18
Calkin algebra on $\mathfrak{h}$       55
Canonical center valued trace      314
Canonical unitary involution of $L^2(\mathcal M, \tau)$       337
Cauchy — Schwarz inequality      37
Cayley transform      81
Center valued trace      298 314
Center valued trace, canonical      314
Central (representing) measure of $\varphi$       247
Central positive linear functionals      343
Central support of a projection      223
Centrally orthogonal projections      292
Closed projections      168
Commutant of $\pi(A)$       53
Complementary split faces      159
Completely positive linear maps      194 200
Components of $\{\pi, \mathfrak{h}\}$       41
Concave functions      158
Conditional expectation of $\mathcal M$ onto $\mathcal N$ with respect to $\tau$       332
Constant field of Hilbert spaces      272
Convex functions      158 231
Cosine of a projection      308
Coupling constants      339
Coupling functions      339
Covariance C*-algebra of $\{\Omega, G\}$       46
Covariance von Neumann algebra of $(\mathcal A, G, \alpha)$       364
Covariant representations      46
Covariant systems      363
Cross-norms      188
Cross-norms, adjoint      190
Cross-norms, greatest      189
Cross-norms, injective      189
Cross-norms, projective      189
Crossed products      364
Cyclic projections      293
Cyclic representation of A induced by $\omega$       41
Cyclic subsets      77
Cyclic vectors      41
Decomposable operators      258
Definition ideal of a trace      319
Diagonal algebras      259 273
Diagonal operators      259 273
Dimension theory      289
Direct integral of measurable fields of Hilbert spaces      272
Direct integral of representations      278
Direct integral of the bounded measurable operator field      273
Direct integral of von Neumann algebras      274
Direct sums      41
Direct sums of von Neumann algebras      73
Disintegration      275
Double commutation theorem      74
Dual C*-algebras      157
Effros Borel structure      264
Enveloping C*-algebra of A      42
Equivalence of projections      290
Ergodic actions      363
Ergodic states      47
Essential space of $\pi$       36
Exponential function      12
Extreme boundary of K      232
Extreme points      47
Extremely disconnected spaces      104
Faces      159
Faces, complementary split      159
Factorial states      248
Factors      72
Faithful linear functionals      36
Faithful representations      36
Faithful semifmite normal traces      309
Faithful traces on a von Neumann algebra      309
Final projections      290
Finite projections      296
Finite traces of a von Neumann algebra      309
Finite von Neumann algebras      296
Fredholm operators      55
Free automorphisms      363
Fundamental sequence of $\mu$ -measurable vector fields      270
G-abelian actions      252
Gelfand representation of A      16
Gelfand — Naimark — Segal construction      41
General linear group      4
Generalized center valued traces      330
Greatest cross-norm      189
Group C*-algebra of G      45
Group measure space construction      374
Group von Neumann algebra of G      364
Groups of infinite conjugacy class      368
Hereditary subcones      146
Hermitian elements      17
Hermitian linear functionals      36
Hermitian sesquilinear forms      59
Hull of m      33
Hyperstonean spaces      107
ICC-groups      368
Identity modulo m      13

Imaginary part of x      17
Index group of A      12
Induced von Neumann algebra of $\mathcal M'$ on $\mathfrak{R}$       76
Induction of $\mathcal M'$ onto $\mathcal M'_e$       76
Infinite projections      296
Infinite von Neumann algebras      296
Initial projections      290
Injective C*-cross-norm      207
Injective C*-tensor products      207
Injective cross-norm      189
Injective tensor products of Banach spaces      189
Integral representations of states      230—253
Invariant subsets      123
Invariant subspaces of $\mathcal M_*$       123
Invertible elements      4
Involutions      2
Involutions, unitary      337
Involutive Banach algebras      2
Irreducible representations      41
Isomorphic von Neumann algebras      72
Joint spectrum of $(a_1, \ldots, a_n)$       80
Jordan decomposition of a finite Radon measure      120
Jordan homomorphisms      187
Jordan product      187
Kadison transitivity theorem      92
Kaplansky density theorem      100
Kernel of $\Gamma$       33
Left invariant subsets      123
Left invariant subspaces      123
Left kernel of $\omega$       37
Left multiplier of A      169
Left regular representation      45
Left support of x      291
Left support projections      140
Liftings      259
Logarithmic function      12
Lower envelope of f      232
Lower semicontinuous functions      104 158
Lusin spaces      378
Matrix units      185
Maximal abelian von Neumann algebras      104
Maximal regular ideals      14
Measurable fields of Hilbert spaces      269
Measurable operator fields      272
Measurable operator valued functions      258
Measurable vector fields      270
Measurable von Neumann algebras      273
Measurable von Neumann algebras, representations      278
Minimal projections      51
Modular lattices      303
Monotone closed C*-algebras      137
Multiplicity of $\pi$       53
Multiplicity-free representations      246
Multiplier algebra of A      169
Multiplier of A      169
n-positive linear maps      194 200
Negative part of h      20
Noncommutative Egoroff's theorem      85
Noncommutative Lusin's theorem      87
Nondegenerate *-algebra of operators      72
Nondegenerate representations      36
Normal elements of involutive algebras      17
Normal linear functionals      127 134 137
Normal measures      106
Normal part of $\omega$       127
Normal representations      128 136
Normal traces on a von Neumann algebra      309
Normalizers      373
Nuclear operators      63
One parameter groups      57
Open projections      168
Operator-monotone functions      93
Operators affiliated with $\mathcal M$       229
Operators of Hilbert — Schmidt class      66 191
Operators of trace class      63
Orthogonal measures      240
Phillips lemma      179
Polar decomposition of $\varphi$       142
Polarization identity      59
Polish spaces      264 375
Positive cones      23
Positive elements      24
Positive linear functionals      36
Positive linear functionals, central      343
Positive linear functionals, tracial      343
Positive part of h      20
Positive sesquilinear forms      59
Predual of $\mathcal M$       127
Predual of a W*-algebra      134
Primary states      248
Primitive C*-algebras      178
Principal component of G(A)      12
Projection lattices      290
Projections      17
Projections, $\alpha$ -homogeneous      299
Projections, abelian      296
Projections, absolutely invariant      363
Projections, centrally orthogonal      292
Projections, closed      168
Projections, cyclic      293
Projections, finite      296
Projections, infinite      296
Projections, minimal      51
Projections, of norm one      131
Projections, open      168
Projections, properly infinite      296
Projections, purely infinite      296
Projective C*-cross-norm      206
Projective C*-tensor products      206
Projective cross-norm      189
Projective tensor products of Banach spaces      189
Proper representations      36
Properly infinite projections      296
Properly infinite von Neumann algebras      296
Pseudoconcentrated measures      246
Pure linear functionals      43
Purely infinite projections      296
Purely infinite von Neumann algebras      296
Quasi-equivalent representations      125
Quasi-spectrum of x      7
Quasi-state space of A      161
Quotient algebras of C*-algebras      31
Radical of A      16
Real orthogonality      223
Real part of jc      17
Real subspaces      223
Reduced von Neumann algebra of M on $\mathfrak{R}$       76
Regular elements      4
Regular ideals      13
Regular subalgebras      373
Representation space      35
Representations      35
Representations, atomic      176
Representations, covariant      46
Representations, faithful      36
Representations, irreducible      41
Representations, multiplicity-free      246
Representations, nondegenerate      36
Representations, normal      128 136
Representations, proper      36
Representations, quasi-equivalent      125
Representations, tensor products of      222
Representations, topologically irreducible      41
Representations, unitarily equivalent      36
Representations, universal      122
Representing measure of a point      233
Resolvant of x      6
Restricted group C*-algebra of G      45
Restriction of n to       204
Resultant of $\mu$       233

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