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| Lance E.C. — Hilbert C*-modules: a toolkit for operator algebraists |
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| Предметный указатель |
"compact operator" 10
"finite-rank" operator 9
 -unital C*-algebra 60 66
Absorption 60
Adjointable map 8
Bounded transform 107
C*-bialgebra 82 121
Cauchy — Schwarz inequality 3
Cayley transform 112
Complemented submodule 21
Completely positive map 39 45—47 78
Completion 4
Comultiplication 82
Conditional expectation 7
Core 97
Corepresentation, unbounded 104—106
Corepresentation, unitary 87
Densely defined operator, non-regular 103
Densely defined operator, regular 96 109—111
Densely defined operator, selfadjoint 101
Densely defined operator, symmetric 101 113
Direct sum 5—6
Essential ideal 14
Exterior tensor product 34—38 62 116
Fully complemented submodule 61
Function C*-bialgebra 83 122
Functional calculus for selfadjoint regular operators 118—120
Hilbert C*-module 4
Hilbert C*-module, countably generated 60 66
Hilbert C*-module, full 69
Idealiser 17
Inner-product C*-module 2
Interior tensor product 38—44 105
Isometry 26
KSGNS construction 50—52
Leg notation 80
| Localisation 7 57
Morita equivalence 74
Morphism of C*-algebras 18
Morphism of C*-bialgebras 82
Multiplier algebra 14—18
Nondegenerate *-homomorphism 15 19
Nondegenerate completely positive map 48—49 53
Partial isometry 29—30 112—115
Polar decomposition 29
Product of sets 15
Quantum group iv 121—122
Reduced convolution C*-bialgebra 83—86 90—93 122
Regular operator 96
Retraction 55
Riesz — Frechet theorem 13
Self-dual Hilbert C*-module 13
Semi-inner-product C*-module 3
Slice map 79
Stabilisation 60
Stable algebra 63 69
Stable isomorphism 69 74
Stable multiplier algebra 63
Stone — Cech compactification 15
Strict completely positive map 49
Strict topology 11 18 76—77
Strictly positive 59
Strictly positive, mod A 108
Tensor product of C*-algebras 31
Tensor product of Hilbert spaces 31
Tensor product, exterior 34—38 62 116
Tensor product, interior 38—44 105
Tietze theorem for C*-algebras 66
Unbounded multiplier 117
Unbounded multiplier, functional calculus 118
Unitary adjointable operator 24
Unitary corepresentation 87—88
Unitary equivalence 24
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