Aliprantis Ch.D. — Positive Operators :: Электронная библиотека попечительского совета мехмата МГУ

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Aliprantis Ch.D. — Positive Operators

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Название: Positive Operators

Автор: Aliprantis Ch.D.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 367

Добавлена в каталог: 01.06.2008

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Предметный указатель

-space      12 187 192
-sum of Banach spaces      176
$\mathfrak{S}$ -topology      142
$\sigma$ -Dedekind complete Riesz space      12
$\sigma$ -ideal      48 93 97
$\sigma$ -order continuity property      96
$\sigma$ -order continuous component      45
$\sigma$ -order continuous dual      56
$\sigma$ -order continuous lattice seminorm      178
$\sigma$ -order continuous operator      42 93
$\tau$ -bounded set      129
$\tau$ -equicontinuous set      142
$\tau$ -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, $\sigma$ -order continuous $E^{\tilde}_c$       56
Dual space, algebraic E*      62
Dual space, order $E^{\tilde}$       55
Dual space, order continuous $E^{\tilde}_n$       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, $l_{\infty}$       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, $\sigma$ -      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, $\sigma$ -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, $\sigma$ -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, $\sigma$ -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 $E^{\tilde}_n$       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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