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| Авторизация |
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| Aliprantis Ch.D. — Positive Operators |
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| Предметный указатель |
 -space 12 187 192
-sum of Banach spaces 176
 -topology 142
 -Dedekind complete Riesz space 12
-ideal 48 93 97
-order continuity property 96
-order continuous component 45
-order continuous dual 56
-order continuous lattice seminorm 178
-order continuous operator 42 93
 -bounded set 129
-equicontinuous set 142
-totally bounded set 129
(u)-property 222
Absolute convex hull 128
Absolute Mackey topology 167
Absolute value of element 4 9 13
Absolute value of operator 9 39 109
Absolute value of set 6
Absolute weak topology 166 169 274
Absorbing set 128
Abstract -space 187 192
Additive operator 7
Adjoint operator 62 92 118 146
AL-space 187 192 249 315
Alaoglu's theorem 141
Algebraic adjoint 62
Algebraic dual 62
Algebraic sum of sets 29 127
AM-space 187 194 254 315
Ando's inequality 46
Annihilator 54
Archimedean Riesz space 7 95 96
atom 105
Balanced set 128
Banach lattice 174 248
Banach space 149
Banach space with Dunford — Pettis property 334
Banach space with property (u) 222
Banach space with reciprocal Dunford — Pettis property 347
Banach space with Schur property 200 338
Banach space, Grothendieck 211
Banach space, reflexive 151 240 287
Banach space, separable 152 153 198
Banach space, weakly compactly generated 308
Banach space, weakly sequentially complete 225 226
Band 30
Band preserving operator 106 250
Band, generated by a set 31 70 84 163 171
Band, generated by an element 35 84
Band, projection 33 69 85
Basic sequence 216
Basis 216
Bipolar of a set 140
Bipolar theorem 140
Boolean algebra 37 191 199
Bounded set, order 10 164
Bounded set, topologically 129 144
Canonical embedding 58
Canonical projection 93
Carrier 47 56
Cartesian product 18
Circled set 128
Clopen set 191
Closed convex circled hull 131
Closed unit ball 150
Compact operator 267 275 279 296
Compatible topology 143
Complement of a subspace 230
Complementable embedding 230 239
Complemented subspace 230
Completion, Dedekind 95
Completion, norm 175
Completion, universal 120 125
Component of element 36
Component of operator 45 75 83 257
Component, elementary 75
Component, simple 75
Consistent topology 143
Convergence of net 30
Convergence of sequence of sets 241
Convergence, order 30
Convergence, uniform 95
Convex circled hull 128
Convex combination 128
Convex hull 128 158
Convex set 24 128
Countable sup property 52 97
Decomposition property 14
Decreasing net 7 167
Decreasing sequence 7
Dedekind complete Riesz space 12 100
Dedekind completion 96 112
Dense set 152 171
Direct sum of Riesz spaces 18 171
Directed set 13
Discrete element 105
Disjoint complement 5
Disjoint elements 5 76
Disjoint sequence 73 180 203 315
Disjoint sets 5
Disjointness preserving operator 107
Downward directed set 13
Dual ball 150
Dual space, -order continuous  56
Dual space, algebraic E* 62
Dual space, order  55
Dual space, order continuous  56
Dual space, second 58 147
Dual space, topological  133 165
Dual system 138 166
Dunford — Pettis operator 333
Dunford — Pettis property 334
Dunford — Pettis set 343
Eberlein — Smulian theorem 156
Element, discrete 105
Element, positive 1
Elementary component 75
Embedding 58 215
Embedding,  217 220 226 235
Embedding,  235 238 241
Embedding,  220 224 235
Embedding, complementable 230 238
Embedding, lattice 215
Equicontinuous set 142
Equivalent bases 217
Equivalent norms 176
Euclidean norm 150
Euclidean topology 150
Extension of an operator 21 51 253
Extension of an operator, positive 24
Extension of an operator, smallest 24
Extremal set 137
Extremally disconnected space 191
Extreme point 25 37 137
F-algebra 116 254
Factorization of an operator 228 293
Family of seminorms 132
Finite rank operator 60 267 272
Freudenthal's Spectral Theorem 82
Full collection of sets 142
Function space 2
Functional, Minkowski 132
Functional, order bounded 55
Functional, order continuous 56
Functional, positive 55
Functional, strictly positive 87 183
Functional, supporting 132
Gantmacher's Theorem 284
Gauge 132
| Generalized orthomorphism 125
Goldstine's Theorem 152
Grothendieck space 211
Hahn — Banach theorem 21
Half-space 137
Homomorphism 88 103 193
Hull, absolute convex 128
Hull, closed convex circled 131
Hull, convex 128
Hull, convex circled 128
Hull, solid 164 202 205
Hull-kernel topology 200
Ideal 23
Ideal in a Boolean algebra 199
Ideal of order boundedness 110
Ideal, - 48 93 97
Ideal, generated by a set 30
Ideal, order closed 30
Ideal, order dense 29
Ideal, principal 31
Ideal, ring 322
Ideal, super order dense 53
Ideal, uniformly closed 95
Identity operator 33 112
Increasing net 7
Increasing sequence 7
Inequality, Ando's 46
Inequality, triangle 6
Infimum of elements 2
Infimum of functionals 55
Infimum of operators 12 38 39 111
interval 10 272
Interval preserving operator 89 197
Interval, weakly compact 179 309
Inverse annihilator 54
Isomorphic Riesz spaces 89
Isomorphism 89
k-disjoint sequence 181
KB-space 225 229 249 287
Kernel 88 113 116 133
Krein — Milman theorem 137
Krein — Smulian Theorem 158
L-weakly compact operator 313
Laterally complete Riesz space 100 120
Lattice embedding 215
Lattice homomorphism 88 99 114 193
Lattice isomorphism 89
Lattice norm 174
Lattice operations 163 196
Lattice seminorm 162
Lattice seminorm, -order continuous 178
Lattice seminorm, order continuous 168 178
Lexicographic plane 19
Linear functional 55 102 133 165
Linear operator 1
Linear topology 128
Locally convex space 131
Locally convex topology 131
Locally convex-solid Riesz space 163
Locally convex-solid topology 163
M-norm 187
M-weakly compact operator 313
Mackey topology 144
Majorizing subspace 26
Maximal ideal in Boolean algebra 199
Mazur's theorem 131
Metrizable topology 153
Minkowski functional 132
Modulus of operator 9 13 39 109 292
Monotone function 22
Multiplication operator 119 252
Negative part of element 4
Negative part of operator 13
Negative part of set 6
Net, decreasing 7
Net, increasing 7
Norm completion 175
Norm, -order continuous 178 197
Norm, Euclidean 150
Norm, lattice 174
Norm, order continuous 178 297
Norm, regular 248
Normed Riesz space 174
Normed vector space 149
Null ideal 47 56 96
o-weakly compact operator 310 339
Operator of finite rank 60 267 272
Operator with order continuous norm 320
Operator, -order continuous 42
Operator, additive 7
Operator, adjoint 62 146
Operator, band preserving 106 250
Operator, compact 267 275 279 296
Operator, dominated by another operator 266
Operator, Dunford — Pettis 333
Operator, interval preserving 89 197
Operator, L-weakly compact 313
Operator, linear 1
Operator, M-weakly compact 313
Operator, multiplication 119 252
Operator, o-weakly compact 310
Operator, order bounded 10
Operator, order continuous 42 93
Operator, positive 2 24 266
Operator, preserving disjointness 107
Operator, regular 10
Operator, semicompact 324
Operator, shift 86
Operator, singular 44
Operator, strictly positive 52
Operator, Tauberian 349
Operator, transpose 62
Operator, weak Dunford — Pettis 342
Operator, weakly compact 284
Operator, weakly continuous 146 283
Order adjoint of an operator 62
Order bounded operator 10 62
Order bounded set 10 164
Order closed set 30
Order continuity property 96
Order continuous component 45
Order continuous dual 56
Order continuous functional 56 65
Order continuous norm 178 287 297 320
Order continuous operator 42 111
Order continuous seminorm 168 178
Order continuous topology 168
Order convergent net 30
Order dense Riesz subspace 29 53 100
Order dual of a Riesz space 55 58 165
Order interval 10 274
Order interval, weakly compact 179 309
Order projection 33 67 85 211
Order unit 188
Order weakly compact operator 310
Ordered vector space 1
Orthomorphism 109 251
Orthomorphism, generalized 125
p-additive norm 187
Perfect Riesz space 59
Phillips' Lemma 233
Point, extreme 25 37 137
Point, quasi-interior 259
Polar of a set 140 171
Positive element 1 163
Positive extension 24
Positive functional 55
Positive operator 2 7 24 266
Positive part of element 4
Positive part of operator 13
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