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| Fell J.M.G. — Induced Representations and Banach *-Algebraic Bundles |
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| Предметный указатель |
 24
 23
 , cross-sectional algebra 134
, transformation algebra 136 262
 space cross-sectional 108
 power summable cross-section 108
 -representation 143
 213
 210
 208
 194
 -bounded 108
 217
 25
*-algebra 24
*-ideal 25
*-representation, abstractly induced 51
*-representation, abstractly induced, compact 85 298
*-representation, abstractly induced, concretely induced 224
*-representation, abstractly induced, conjugate under a group element 301
*-representation, deduced 46
*-representation, deduced, faithful 26
*-representation, deduced, generated by a completely positive linear map 46
*-representation, deduced, generated by a positive linear functional 156 157
*-representation, deduced, inducible 51 81
*-representation, deduced, integrated form of 150
*-representation, deduced, of  , induced 273
*-representation, deduced, of a *-algebra 26
*-representation, deduced, of a Banach *-algebraic bundle 140
*-representation, deduced, of the multiplier bundle 146
*-representation, deduced, positive with respect to Banach *-algebraic bundle 198
*-representation, deduced, rigged space or module 49
*-representation, deduced, space of 26 140
*-representation, deduced, zero 26
*-seminorm 95
Action of a multiplier, left and right 120
Admissible functional 26
Annihilator 122
Approximate unit 116
Associated with a *-representation 189
Banach 100
Banach *-algebra 25
Banach *-algebra,  -completion of 168
Banach *-algebra, reduced 160
Banach *-algebraic 112
Banach *-algebraic bundle 112
Banach *-algebraic bundle, *-representation of 140
Banach *-algebraic bundle, approximate unit of 116
Banach *-algebraic bundle, homogeneous 123
Banach *-algebraic bundle, isometric isomorphism of 115
Banach *-algebraic bundle, isomorphism of 115
Banach *-algebraic bundle, reduction of 114
Banach *-algebraic bundle, retraction of 114
Banach *-algebraic bundle, saturated 115
Banach *-algebraic bundle, unit element of 116
Banach *-algebraic bundle, unit fiber *-algebra of 115
Banach *-algebraic bundle, with enough unitary multipliers 123
Banach *-algebraic, -completion 171
Banach *-algebraic, cross-section of 100
Banach *-algebraic, Hilbert 100
Banach *-algebraic, projection 99
Banach *-algebraic, space 99
Banach *-algebraic, trivial 101
Banach *-algebraic, with enough continuous cross-sections 100
Banach bundle 100
Banach bundle, reduction of 101
Base space 99
Basic conditional expectation 198
Blattner inducing construction 231
Block *-subalgebra 74
Bochner integral 110
Bounded functional 181
Bounded functional, map 119
Bounded functional, module 46
Bundle 99
C(B) 103
C(M) 24
C(M;X) 23
C*-algebraic bundle 124
C*-algebraic bundle, saturated 175
C*-algebraic bundle, structure 173
C*-completion of a Banach *-algebra 168
C*-cross-sectional algebra 173
Canonical imprimitivity bimodule 279
Canonically constructed saturated bundle 321
CAR algebra 177
Circle extension bundle 129
Cocycle representation 144
Commuting algebra 28
Compact *-representation 85 2
Compact operator 25
Compact operator, inner product 42
Compacted cross-sectional algebra 134
Compacted integrated form of a system of imprimitivity 269
Compacted transformation algebra 136 262
Complete positivity 28
Completely positive linear map 46
Complex-conjugate imprimitivity bimodule 73
Complex-conjugate imprimitivity bimodule, linear space 23
Complex-conjugate imprimitivity bimodule, modules 73
Composition of rigged modules 58
Composition of rigged modules, reduced 59
Concretely induced *-representation 224
Conditional expectation 50
Conditional expectation, basic 198
Conjugate *-representation 301
Convolution (generalized) 134
Covariance algebra 135
Cross-section 100
Cross-section, locally measurable 108
Cross-section, p power summable 108
Cross-sectional space 108
Cross-sectional algebra, 173
Cross-sectional algebra, , compacted 134
Cross-sectional algebra, , discrete 141;
Deduced Hilbert space 31
Deduced Hilbert space, *-representation 46
Deduced Hilbert space, operator inner product 37
Deduced Hilbert space, pre-*-representation 45
Degenerate 26
Direct limit of C*-algebras 177
Direct product bundles 127
Direct sum Hilbert 27
Discrete cross-sectional *-algebra 141
Dual operator inner product 40
Enough continuous cross-sections 100
Enough unitary multipliers 123
Essential space 26
Extension of a *-representation to multiplier algebra 146
Extension of a *-representation to multiplier algebra, multiplier bundle 147
Faithful 26
Fiber 100
Functional of positive type 181
Functional of positive type, associated with a *-representation 189
Generalized regular representation 162
Generated *-representation by a completely positive map 46
Generated *-representation by a completely positive map, by a positive functional 156 157
Glimm algebra 177
Group bundle 127
Group extension 24
Group extension, bundle 129
Group extension, central 24
Group extension, isomorphic 24;
| Group extension, trivial 24
Hermitian module 44
Hilbert bundle 100
Hilbert bundle, induced by a *-representation 209
Hilbert direct sum of operator inner products 34
Hilbert direct sum of operator inner products, *-representations 27 142
Homogeneous Banach *-algebraic bundle 123
Imprimitivity *-algebra 76
Imprimitivity bimodule 72
Imprimitivity bimodule, canonical 279
Imprimitivity bimodule, complex-conjugate 73
Imprimitivity bimodule, inducible with respect to 81
Imprimitivity bimodule, positive with respect to 81
Imprimitivity bimodule, strict 73
Imprimitivity bimodule, topologically strict 87
Imprimitivity, system of 86 265 266
Induced *-representation, abstract 51
Induced *-representation, Blattner formulation of 231
Induced *-representation, concrete 224
Induced *-representation, Mackey formulation of 233
Induced *-representation, of 273
Induced Hilbert bundle 209
Induced system of imprimitivity 273
Inducible with respect to an imprimitivity bimodule 81
Inducible with respect to an imprimitivity bimodule, a rigged module 51
Inductive limit topology 106
Inner hull-kernel topology 71
Integrated form of a multiplier 138
Integrated form of a multiplier, *-representation 150
Integrated form of a multiplier, system of imprimitivity 269
Intertwining operator for operator inner products 29
Intertwining operator for operator inner products, *-representations 26 142
Irreducible 26 142
Isometric 115
Isomorphism of Banach *-algebraic bundles 115
Isomorphism of group extensions 24
L(B) 103
L(B), integrated form 150
L(M) 24
L(M;X) 24
Left action of a multiplier 120
Left order 119
Linear functional on a bundle 180
Locally convex space 25
Locally measurable cross-section 108
Mackey inducing construction 233
Module 25
Module, bounded 46
Module, Hermitian 44
Multiplier 120
Multiplier, *-algebra 121
Multiplier, *-algebra, extension of *-representation to 146
Multiplier, bundle 121
Multiplier, bundle, extension of *-representation to 147
Multiplier, enough unitary 123
Multiplier, integrated form of 138
Multiplier, order of 120
Multiplier, unitary 122
Non-degenerate 26 142
Non-degenerate, (system of imprimitivity) on  288
O(X) 25
O(X, Y) 25
Operator inner product 28
Operator inner product, compact 42
Operator inner product, deduced 37
Operator inner product, Hilbert direct sum of 34
Operator inner product, tensor product of 35
Order 113
Order, left 119
Order, of a multiplier 120
Order, right 119
P(B) 18 2
Positive *-representation with respect to Banach *-algebraic bundle 198
Positive *-representation with respect to Banach *-algebraic bundle, imprimitivity bimodule 81
Positive *-representation with respect to Banach *-algebraic bundle, rigged space or module 49
Positive linear functional, *-representation generated by 156 157
Positive type, functional of 181
Positivity, complete 28
Pre-*-representation 25
Pre-*-representation, deduced 45
Primitive -algebra 175
Projection-valued measure 265
Projective representation 144
Quasi-linear 119
Quotient topology 71
Reduced Banach *-algebra 160
Reduction of a Banach *-algebraic bundle 114
Reduction of a Banach *-algebraic bundle, bundle 101
Regional topology for *-representations of *-algebras 61
Regional topology for *-representations of *-algebras, bundles 180
Regular projection-valued measure 265
Regular representation, generalized 162
Representation, projective 144
Retraction of a Banach *-algebraic bundle 114
Retraction of a Banach *-algebraic bundle, bundle 101
rho-function 193
Rigged modules 50
Rigged modules, composition of 58
Rigged modules, positive with respect to 51
Rigged modules, reduced composition of 59
Rigged space 47
Rigged space, positive with respect to 49
Rigging 47
Right action of a multiplier 120
Right order 119
Saturated Banach *-algebraic bundle 115
Saturated Banach *-algebraic bundle, -algebraic bundle structure 175
Saturated Banach *-algebraic bundle, canonically constructed 321
Semidirect product bundle 126
Seminorm 25
Seminorm, topology generated by a family of 25
Space of a *-representation 26 140
Spherical function 94
Stable subspace 26 142
Strict imprimitivity bimodule 73
Strict imprimitivity bimodule, topologically 87
Strong multiplier topology 121
Structure space 70
Subrepresentation 26 142
Summable vector-valued functions 110 111
Support 103
System of imprimitivity 86 265 266
System of imprimitivity, induced 273
System of imprimitivity, transformation bundle form of 269
Tensor product of operator inner products 35
Tensor product of operator inner products, representations 143
Topologically strict imprimitivity bimodule 87
Topology generated by a family of seminorms 25
Transformation algebra 78
Transformation algebra, 136 262
Transformation algebra, compacted 136 262
Transformation bundle 128 260
Transformation bundle, form of a system of imprimitivity 269
Transversal 24
Trivial bundle 101
Trivial group extension 24
Unit element of a Banach *-algebraic bundle 116
Unit fiber *-algebra 115
Unitary equivalence 26 29 14
Unitary multiplier 122
Unitary representation 27
Weak containment 67
Zero representation 26
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