Lindenstrauss J., Tzafriri L. — Classical Banach Spaces I, II :: Электронная библиотека попечительского совета мехмата МГУ

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Lindenstrauss J., Tzafriri L. — Classical Banach Spaces I, II

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Название: Classical Banach Spaces I, II

Авторы: Lindenstrauss J., Tzafriri L.

Язык:

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: reprint of the 1977 edition

Год издания: 1977

Количество страниц: 243

Добавлена в каталог: 12.04.2005

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(u), property      31 32 34
Absolutely summing operators      see "Operators"
Approximation property (A.P.)      33 102 113
Approximation property, bounded (B.A.P.)      112
Approximation property, compact (C.A.P.)      102 103 107 111
Approximation property, metric (M.A.P.)      33
Averaging operators      see "Operators"
Banach lattice      1—4 6 7 13 18 22 29 31 45 79 93 102
Banach lattice, $\sigma$ -order complete      4—10 12 14 15 20 25 26 29 34 38 83 89 114 118
Banach lattice, $\sigma$ -order continuous (norm in a)      7 9 14 22 25 26 29 34—36 38 83 121
Banach lattice, atom of a      20
Banach lattice, band of a      3 9 10 23 24 35 85
Banach lattice, canonical embedding of a (in its second dual)      4 17 27 28 34 35
Banach lattice, characterizations of an order continuous      7 8 10 25 27—29
Banach lattice, complexification of a real      43
Banach lattice, definition of      1
Banach lattice, disjoint elements in a      2 6 7 9 20—24 38 39 52 82 84 89 91 141 157 165 181 182 188 198—200
Banach lattice, dual of a      3 4 17 24 25 29 83 84 96 97 121
Banach lattice, functional representation of a      25 27 28 35 36 39 40 52 83
Banach lattice, lower q-estimate (for disjoint elements) of a      79 82—85 88—92 97—99 130 132 139 140 231
Banach lattice, lower q-estimate constant of a      83
Banach lattice, monotone sequences in a      3
Banach lattice, norm-bounded sequences in a      34 35
Banach lattice, order bounded sets in a      3—8 29
Banach lattice, order complete      4 6 8 10 20 35 85
Banach lattice, order continuous (norm in a)      7 8 10 12 14 15 19 21 25—29 31 32 34—40 83 89 118 186 232
Banach lattice, p-convex      40 45 46 49 51—55 57 59 73 79—82 85 87—90 95—99 133 181 188 191 194—198 209 220—223 231
Banach lattice, p-convexification of a      53 55 58 81 89 98 99 201
Banach lattice, p-convexity constant of a      46 51 81 99 138 189 191 194 195 197
Banach lattice, projection band of a      9—11 25 34 35
Banach lattice, q-concave      40 45 46 49—51 53—56 59 73 74 79—82 85 88 92 93 95—98 126 133 162 169 170 174—176 181 186—188 195 197 198 200 201 209 220—223
Banach lattice, q-concavification of a      54 55 88 201 221 222
Banach lattice, q-concavity constant of a      46 51 77 81 133 189 193
Banach lattice, second dual of a      4 84 85
Banach lattice, separable      7 12 25 29 38 52 83 89 118 121
Banach lattice, sublattices of a      3 19 22 51 55 59 103
Banach lattice, subspaces of a      31 34 35 37—39 51 98 102 189
Banach lattice, units of a      see "Strong unit and weak unit"
Banach lattice, upper p-estimate (for disjoint elements) of a      79 82—85 87 88 90 96 97 130 132 139 140 195 197 200 201 231
Banach lattice, upper p-estimate constant of a      83 202
Banach lattices, interpolation pair of      see "Interpolation"
Band      see "Banach lattices"
Basis, block basis of a      158 161 198
Basis, monotone      150 151 231 232
Basis, perfectly homogeneous      24
Basis, perturbation of a      38 176 179
Basis, precisely reproducible      158 162 189 190 195 198 200 201
Basis, reproducible      150 158 162
Bohnenblust's characterization of abstract $L_{p}$ and M spaces      18
Boolean algebras of projections      see "Projections"
Boolean algebras, Stone's representation theorem for      see "Stone"
Boolean operations      114
Boyd indices      129—131 134 139 142 144 147 157 162 167 168 175 179 188 199 200 202 212 219 220
Boyd interpolation theorem      see "Interpolation"
C*-algebra, commutative      17
Caratheodory extension theorem      15
Cauchy — Schwarz inequality      155 167
Central limit theorem      135 136
Concave Banach lattice      see "Banach lattice q-concave"
Concave operators      see "Operators q-concave"
Concavification of a Banach lattice      see "Banach lattice q-concavification
Condition $\Delta_{2}$       64 115 120 199
Conditional basis      162
Conditional expectation      122 128 151 179 215
Cone, positive      2 3 7 12 17 36 44
Convex Banach lattice      see "Banach lattice p-convex"
Convex operators      see "Operators p-convex"
Convexification of a Banach lattice      see "Banach lattice p-convexification
Convexification, uniform      216 231
Convexity, modulus of      59 63 65—72 78—80 88 90 97 99 229
Convexity, strict      60—62
Convexity, uniform      40 59—63 69 77 79—81 88 90 97 102 162 199 202 228 229 231 232
CoType      59 72—74 77—79 82 88 90 93 96—99 102 111 181 189 208 231
Cotype, constant      73
Cyclic space      12—16 20 26
Cyclic vector      12
Decomposition method      see "Pelczynski's decomposition method"
Decomposition property      2 22 26 36 88 125 221
Differentiability, Frechet      61
Differentiability, Gateaux      61
Distribution function      116 117 132 141 142 157 160 170 205—207 209 211
Distribution, normal      135 213
Distribution, Poisson      204 205 214
Distribution, uniform      205
Distribution, vectors with the same      140—142 157 158 160
Doob's maximal inequality      153 155
Dvoretzky's theorem      63
Eberlein's theorem      35
Equi-integrable sets      216 223
Estimate, lower      see "Banach lattice lower
Estimate, upper      see "Banach lattice upper
Extreme points      121 124 159
Factorization of weakly compact operators      216 224
Factorization theorems      57 59 95
Fatou property      30 118—121 123 128
Fourier transform      182
Function, homogeneous of degree one      40 42 44
Function, locally integrable      29 142
Function, spaces      see "Koethe Lorentz Orlicz
Function, square      126 154 156 166
Functional calculus      42 43
Functional, Hahn — Banach      25
Functional, strictly positive      25—27
Greatest lower bound (g.l.b)      1 8 21
Grothendieck's inequality      93 94
Grothendieck's universal constant      93 94 173
Haar system      2 150 151 154—158 160—162 165 168 175—179 181 182 186 187 198—200 223
Hoelder inequality      44 53 56 89 106 143 154 174 209
Hoelder type inequalities      43 49 76
Ideal      see "Banach lattices"
Independent random variables      see "Random variables"
Integrals      see also "Space X' of integrals" 29
Interpolation method of Lions — Peetre      149 216 225 227—229 231 232
Interpolation pair of Banach lattices      218 219 221 231 232
Interpolation pair of spaces      216—218 225 227—230
Interpolation theorem, Boyd      144 147 156 168 209
Interpolation theorem, Marcinkiewicz      130 149 153 228
Interpolation theorem, Riez — Thorin      149 156 166
Interpolation theorems      114 123 124 126 127 129 130 142 144 171 215
Interpolation, real method in      216
Interpolation, spaces      215 216 218 219 227 228 230—232
Kakutani's representation theorem for abstract $L_{p}$ spaces      15 18 24 93 95
Kakutani's representation theorem for abstract M spaces      16 18 24 93 94
Khintchine's inequality      39 49 50 70 134 169 174 186 187 204
Khintchine's inequality, two dimensional      173 174
Koethe function spaces      14 28—31 36 38 83 89 104 114—118 121 123 127—130 164 188 216 218 223
Kolmogorov's consistency theorem      205
Krein — Milman theorem      121 159
Krivine's theorem      72 111 141
Lattices      see "Banach and vector lattices"
Least upper bound (l.u.b)      1 3—6 8 29 35 42
Liapounoff's theorem      158
Lions — Peetre interpolation      see "Interpolation method of Lions — Peetre"
Lorentz spaces      64 88 97—99 120 121 129 132 133 142
Lorentz spaces, modulus of convexity of      67 71 72
Lower q-estimate      see "Banach lattice lower
Marcinkiewicz interpolation theorem      see "Interpolation"
Marcinkiewicz weak type, operators of      see "Operators of Marcinkiewicz weak type"
Martingale      150—156
Matrices      123 124 138 173
Maurey — Rosenthal example      39 231
Measure space, automorphism of a      114—116 118 127 138 149 151 186
Measure space, complete      29
Measure space, separable      114
Modulus of convexity      see "Convexity modulus
Modulus of smoothness      see "Smoothness modulus
Norming subspace      29 30 118
Operators of Marcinkiewicz weak type      144 145
Operators of strong type      144 149 150 156
Operators of weak type      130 142 144 145 147—149 153 156 167 228

Operators, automatic continuity of positive      2
Operators, averaging      122
Operators, compact      33
Operators, diagonal of      21
Operators, dilation      130 131 163 170 206 219
Operators, finite rank      33
Operators, multiplicity theory-for spectral      11
Operators, norm $\| T\|_{1,2}$ of      217—219
Operators, order preserving      2
Operators, p-absolutely summing      56 57 93
Operators, p-convex      45 47—49 55 57 59 95
Operators, positive      2 4 55—57 59 95 115 125
Operators, q-concave      46 48 49 55—57 59 95
Operators, quasilinear      126 127 147 149 153 228
Operators, simultaneous extension      21 22
Operators, weakly compact      216 224
Order interval      28
Order isometry      3 4 15—17 19 25 29 36 41 44 58 118 190 211
Order isomorphism      2 3 22 24 26 35 121 185
Order like relation      123 125
Orlicz functions      64 65 119 120 134 164 220
Orlicz spaces      67 115 120 131 134—136 139 140 162 163 165 181 187 188 199 200 209 223
Orlicz spacesá modulus of convexity of      67 71 72
Partition of unity      94
Pelczynski's decomposition method      172 209 220 222
Polar $Y^{\bot}$ of a band Y      9 10 20 26 27 36
Primary space      168 179
Process with independent increments      204 206 213
Process, Poisson      202 204—207 212 213
Process, r-stable      213
Process, stationary      204 206 213
Process, symmetric      206 213
Projections of the form Px      8—10 12 13 15 16
Projections, $\sigma$ -complete B.A. of      11—13 26
Projections, band      10 11 23—25 85
Projections, Boolean algebra (B.A.) of      11 12 14 15 20
Projections, contractive      8 10 19—21 122 123 209
Projections, orthogonal      137 138 171 172 209
Projections, positive      8 10 19 20
Projections, Riesz      166—168
Quotient space      3
Rademacher elements      92 93
Rademacher functions      29 51 72—74 77 85 104 106 134 136—138 160 162 169 198 204 213
Radon — Nikodym derivative      31
Radon — Nikodym property      69
Radon — Nikodym theorem      27 29 122
Random variables, characteristic functions of      204 205
Random variables, independent      85—87 135 160 182 185 204—207 213 214
Random variables, p-stable      181 182 185 213
Random variables, symmetric      206 207 214
Rearrangement, decreasing      117 123 125
Rearrangement, invariant (r.i.) function space      40 114 115 117—123 125 126 130—134 136 138 141 145 149—151 156 158 161 162 165—170 176 178 181—183 190 191 198—200 204 207 209 211 220
Rearrangement, invariant (r.i.) function space, analytic part of a      168
Rearrangement, invariant (r.i.) function space, complemented subspaces of a      168 170 172 175 176 178 195 199 200 209
Rearrangement, invariant (r.i.) function space, maximal      118—123 126 128 136 147 204 205 211 219
Rearrangement, invariant (r.i.) function space, minimal      118—121 123 126 128 133 147 204 205 211 219 220 223
Reflexivity      33 35 47 61 62 69 78 224 225 231
Reflexivity in Banach lattices      4 22 31 35 37
Reflexivity in r.i. function spaces      119 132 181 188 199 200
Renorming theorems      54 55 80 88 90 115
Riemann — Stieltjes integral      12 14
Riesz — Thorin interpolation theorem      see "Interpolation"
Schauder decomposition      111
Schauder decomposition, finite dimensional (F.D.D.)      33 34
Schauder decomposition, unconditional      33
Separation theorem      30 58 124
Smoothness      60 61
Smoothness, modulus of      59 63 64 67 68 70 71 78—80 88 90 229 230
Smoothness, uniform      59—63 69 77 80 88 90 229
Space $C(\beta N)$       6
Space $c_{0}$       6 7 16 20 22 24 27 34—37 46 52 57 78 89 93 96 119 127 128 158 187
Space $c_{0}(X)$       46 47
Space $c_{0}(\Gamma)$       7 9 20 22 24
Space $H_{p}$       168
Space $K(X_{1}, X_{2}, Y, \{a_{n}\}, \{b_{n}\})$ (also $\widetilde{K}(X_{1}, X_{2}, Y, \{a_{n}\}, \{b_{n}\})$ )      218—221
Space $l^{n}_{1}$       62 74 90 92—94 124 141 157 197 201
Space $l^{n}_{2}$       63 93 112 194 200—202
Space $l^{n}_{p}$       20 111 112 194
Space $l^{n}_{\infty}$       41 74 90 92—94 124 141 157 182 198
Space $l_{1}$       35 36 78 82 93 118 126 132 160 161
Space $L_{1}(-\infty,+\infty)$       182
Space $L_{1}(0,1)$       2 4 78 118—122 125 127 128 130 156 161 167 187 191 200 215
Space $L_{1}(0,\infty) + L_{\infty}(0,\infty)$       118—120 123 125 127 132 217
Space $L_{1}(0,\infty) \bigcap L_{\infty}(0,\infty)$       118 119 123 132
Space $L_{1}(X)$       77
Space $L_{1}(\mu)$       17 25—27 29—31 35 38 39 44 93 94 153 208
Space $L_{2}(X)$       67—69 78 229
Space $l_{M}$       see "Orlicz spaces"
Space $L_{p,q}$       142—144 148 212 228
Space $l_{p} \oplus l_{2}$       213
Space $l_{p}$       15 22—24 46 81 87 107 108 158 178 182 195 211 213 222
Space $l_{p}$ , modulus of convesity of the      63 71 72
Space $l_{p}$ , modulus of smoothness of the      63 71
Space $L_{p}(0,1)$       2 52 63 75 77 102 106 129 134 140 151 156 161 162 166 168 169 171 172 175 178 181 182 188—191 198—200 202 203 209 211—214 223 231
Space $L_{p}(0,\infty) + L_{q}(0,\infty)$       132—134 149 191 202 209 218
Space $L_{p}(0,\infty) \bigcap L_{q}(0,\infty)$       132—134 147 189 191 202 209 213 214 218
Space $L_{p}(l_{2})$       171 172
Space $l_{p}(X)$       46—48 83 193 201
Space $L_{p}(X)$ (also $L_{p}(R,X)$ )      170 225—227 229
Space $L_{p}(\mu)$       2 4 9 10 12 13 15 16 19 20 22 38 43 45 53 55 57 59 73 114 120 142—144 153 168 182 202 207 208
Space $L_{p}(\mu)$ , modulus of convexity of the      63 72 81
Space $L_{p}(\mu)$ , modulus of smoothness of the      63 72
Space $L_{p}(\mu)$ , sublattices of the      16
Space $l_{\infty}$       6 7 13 30 36 115 118
Space $L_{\infty}(0,1)$       7 118—122 126—127 130 134—136 150 160 161 183 191 215
Space $l_{\infty}(X)$       47
Space $l_{\infty}(\Gamma)$       6 7 26
Space $L_{\infty}(\mu)$       17 25 30 44 73 96 159 214
Space $U_{p,q}$       222 223
Space $X(c_{0})$       46 ?7 85
Space $X(l_{2})$ (also $\widetilde{X}(l_{2})$ )      168—176 179 180
Space $X(l_{p})$ (also $\widetilde{X}(l_{p})$ )      46—48
Space $X(l_{\infty})$ (also $\widetilde{X}(l_{\infty})$ )      46 47
Space $X_{1} + X_{2}$       217 218
Space $X_{1} \bigcap X_{2}$       217 218 226 227
Space $X_{p,2,w}$ (also $X_{p,2}$ )      213 214
Space $X_{Y,\sigma}$       214 215
Space $[X_{1},X_{2}]_{\theta,p}$       226—228 230 231
Space C(0,1)      2 4 10 13 36 52 62 114 162 167
Space C(K)      2 4—6 14 16 17 20 41—43 56 57 93 94 96
Space C(K), sublattices of the      16 20 41
Space J      36 39
Space Rad X      169—172
Space X' of integrals      29—31 117—121 137
Space, abstract $L_{1}$       17 23 24 44 95
Space, abstract $L_{p}$       14 15 18 21 22 24 58
Space, abstract M      9 14 16—22 24 41 73
Space, Hilbert ( $l_{2}$ , $L_{2}(0,1)$ , etc)      52 63 73 74 96 105 106 111 134—137 154 162 163 165 166 181 188 190 191 195 196 198 199 202 203 209 213
Space, partially ordered      1
Stone's representation theorem for Boolean algebras      15
Stopping time      152 153
Strong type operators      see "Operators"
Strong unit      9 16 17 41
Subsymmetric basis      158
Symmetric basis      97 99 114 115 119 122 124 127 128 160 162 188
Symmetric basis, block bases generated by one vector of a      140
Symmetric basis, block bases with constant coefficients of a      121
Topological space $\beta N$       5
Topological space, basically disconnected      4 5
Topological space, extremally disconnected      4 5
Topological space, totally disconnected      15 26
Tree of subsets      178 179
Trigonometric system      150 165—167
Tsirelson's example      81
Tychonoff's theorem      20
TYPE      59 72—74 77—79 82 88 90 92 93 96 97 102 111 112 181 188 195 197 200 201 207 209 230 231
Type power      63 78—80 88 90
Type, constant      73 79 112 195
Type, duality of the      79 96
Ultrapower      213

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