Sakai S. — C*-algebras and W*-algebras :: Электронная библиотека попечительского совета мехмата МГУ

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Sakai S. — C*-algebras and W*-algebras

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Название: C*-algebras and W*-algebras

Автор: Sakai S.

Аннотация:

Presents for study operator algebras in Hilbert spaces, Rings of operators or von Neumann algebras & Banach algebras.

Язык:

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1971

Количество страниц: 256

Добавлена в каталог: 15.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\natural$ -operation      93
$\sigma$ -topology      2 14
$\sigma$ -weak operator topology      34
$\tau$ -topology      21
$\varepsilon$ -central sequence      184
${C}^{*}$ -algebra      1
${C}^{*}$ -algebra of all compact linear operators      46
${C}^{*}$ -norm      60
${C}^{*}$ -seminoma      220
${C}^{*}$ -subalgebra      2
${C}^{*}$ -tensor product      66
${s}^{*}$ -topology      20
${W}^{*}$ -algebra      1
${W}^{*}$ -algebra generated by a set      18
${W}^{*}$ -algebra on a Hilbert space      103
${W}^{*}$ -homomorphism      140
${W}^{*}$ -infinite tensor product      202
${W}^{*}$ -representation      40
${W}^{*}$ -subalgebra      2
${W}^{*}$ -tensor product      67
*-automorphism      119
*-homomorphism      4 5
*-isomorphic      4
*-isomorphism      4 5
*-representation      40 50
*-representation constructed via a state      40
Abelian projection      85
Absolute of linear functional      32
Absolute value      8 27
Adjoint      9 33
Adjoint operation      33
Amenable ${C}^{*}$ -algebra      240
Amenable group      150 209
Amplification      102
Anti-isomorphic      113
Associated closed operator to a ${W}^{*}$ -algebra      106
Asymptotically abelian ${C}^{*}$ -algebra      128
Asymptotically abelian ${W}^{*}$ -algebra      214
atomic      237
Automorphism      153
B T theorem      106
Bicommutant      48
C-isomorphism      123
C-measure      122
Canonical ${W}^{*}$ -infinite tensor product      214
Central decomposition      125
Central decomposition of states      125 146
Central homomorphism      147
Central measure      125 147
Central projection      25
Central sequence      183 197
Central support (envelope)      25
Centrally orthogonal      148
Classification of ${W}^{*}$ -algebras      83
Commutant      48
Commutation theorem of tensor products      108
Commutation theorem of von Neumann      48
Commutative ${C}^{*}$ -algebra      3
Commutative ${W}^{*}$ -algebra      45
Comparability theorem      79 80
Complete additivity      30
Composition series      235
Concrete ${C}^{*}$ -algebra      33
Concrete ${W}^{*}$ -algebra      33
Condition of Glimm      221
Conditional expectation      101
Continuous ${W}^{*}$ -algebra      86
Countably decomposable      80
Coupling function      115 116 117
Criterion of Types      95
Cross norm      58
Cyclic      50
Cyclic projection      116
Cyclic vector      50
Decomposition of States      121 140
Derivation      153
Diagonalizable operators      134
Direct integral of Hilbert spaces      137
Direct sum      2
Discrete ${W}^{*}$ -algebra      86
Disjoint      148
Equivalence of central sequences      183
Equivalence of projections      79
Equivalence of representations      51
Ergodic      126 175
Ergodic decomposition      127 175
Ergodic state      120
Extremal decomposition      123
Extreme points      10
Factor      80
Factorial representation      142
Factorial states      125
Faithful family of representations      5 3
Faithful family of states      31
Faithful representation      41
Faithful state      31
Faithful trace      95
Final projection      3
Finite ${W}^{*}$ -algebra      83 89
Finite projection      83
Finite trace      95
free      175
G-abelian system      126
Glimm's condition      221
Global ${W}^{*}$ -algebras      216
Greatest cross norm      58
Group ${C}^{*}$ -algebra      217 220
Hilbert — Schmidt class      35
Homogeneous projection      88
Homomorphism      3
Hyper — Stonean      46
Hypercentral sequence      213
Hyperfinite factor      204
Ideal      24
Increasing directed set      6 15
Induction of representation      102

Inductive limit of ${C}^{*}$ -algebras      70 71
Inductive limit of states      74
Infinite conjugacy group      182
Infinite product state      75
Infinite projection      83
Infinite tensor product of ${C}^{*}$ -algebras      70 75
Initial projection      3
Inner asymptotic abelianness      215
Inner derivation      153
Invariant      19
Involution      1 111
Irreducible *-representation      52
Isomorphism      4
Kaplansky's density theorem      22
Kernel of *-representation      54
Least cross norm      58
Left support      25
Localizable      45
Locally countably decomposable      117
Mackey topology      19
Measurable      175
Measurable family of ${W}^{*}$ -algebras      136
Measurable family of Hilbert spaces      138
Minimal projection      132
Non-measurable      175
Norm      1
normal      3
Normal linear functional      30
Normal positive linear functional      28
Normal trace      95
Nowhere trivial ^representation      51
Orthogonal      31
Orthogonal decomposition      8 31
Outer automorphism      166
Outer derivation      153
Partial isometry      3
Polar decomposition of linear functional      31 32
Polar decomposition of operators      27 109
Polish space      141
Positive element      7
Positive linear functional      9
Powers' factors      207
Predual      1
Projection      3
Properly infinite      84
Property P      207
Pure state      53
Purely infinite      83
Quasi-equivalent      54
Quasi-invariant measure      175
Radon — Nikodym theorems in ${W}^{*}$ -algebras      75
Reduction theory      131
Regular maximal left ideal      5 8
Representation theorems for ${C}^{*}$ -algebras and ${W}^{*}$ -algebras      40
Residual      184
Right support      25
S-topology      20
Second dual of ${C}^{*}$ -algebras      42
Self-adjoint      2 3 9 19
Semi-central measure      148
Semi-finite      84
Semi-finite trace      95
Separating vector      50
SIMPLE      74
Smooth      221
Spatial isomorphism      111 118
Spectral resolution      26
Spectrum      3
Spectrum space      4
Standard representation      111
State      10
State space      41
Stone — Weierstrass theorem for ${C}^{*}$ -algebras      236
Stonean space      6
Strong *-topology      20
Strong operator topology      33
Strong topology      20
Strongest operator topology      33
Strongly residual      184
Strongly residual sequence      185
Subrepresentation      51
Sum of representations      51
Support of ${W}^{*}$ -representation      54
Support of normal state      31
Support of normal trace      97
Support of operators      25
Tensor product of ${C}^{*}$ -algebras      58
Tensor product of ${W}^{*}$ -algebra      58
Trace class      36
Traces      95
Tracial decomposition      130
Tracial state      90
Trivial central sequence      213
Type $({p}_{1}, {p}_{2}, ...),$       24
Type ${II}_{1} {W}^{*}$ -algebra      86
Type ${II}_{\infty} {W}^{*}$ -algebra      86
Type ${I}_{n} {W}^{*}$ -algebra      88
Type ${P}_{\gamma}$       111
Type ${S}_{\gamma}$       115
Type I ${C}^{*}$ -algebra      219 221
Type I ${W}^{*}$ -algebra      86 87
Type I *-representation      221
Type I group      220
Type II ${W}^{*}$ -algebra      86
Type II *-representation      221
Type III ${W}^{*}$ -algebra      86
Type III *-representation      221
Type of Tensor products of {W}^{*}$-algebras      98
Uncountable families of factors of type ${II}_{1}, {II}_{\infty}, III$       183
Uniform topology      2 33
Uniformly hyperfinite      73
Unitary      3
Universal *-representation      41
Vector state      103
Weak operator topology      34
Weak topology      2 14
Weakly closed self-adjoint algebra      35

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