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Harmand P., Werner D., Werner W. — M-Ideals in Banach Spaces and Banach Algebras |
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Предметный указатель |
-spaces 306—321 324 336—339
-ball property 95—96
-subspaces 78 131
-spaces vs. -spaces 91
-spaces, centralizer of 90
-spaces, definition 83
-spaces, structure topology of 95
-spaces, ultraproducts of 91
-preduals 81—92
-preduals and intersection properties of balls 99
-preduals and M-embedded spaces 119
-preduals, complex 99—100
-projections 45
-subspaces 131 170 176 208 314 318 324 331
-summands 45
-ideals 211—214
-ideals of compact operators 343—344
-closed set 183
-continuous functional 186
-space 96
3-ball property 19
3-ball property vs. 2-ball property 22 99
3-ball property, restricted 19
Ace of diamonds lemma 170
Annihilator 1
AP (see Approximation property)
Approximate unit 217
Approximation of the identity shrinking compact 298
Approximation property 58
Approximation property, bounded 58
Approximation property, compact 58
Approximation property, metric 58
Approximation property, metric and M-embedded spaces 118
Approximation property, metric compact 58 294
Approximation property, metric compact and M-embedded spaces 118
Approximation property, metric compact and M-ideals of compact operators 295 301 306
Approximation property, metric compact unconditional 343
Approximation property, metric, unconditional 343
Arens multiplication 216
Arens regularity 216 219 250
Asplund space 126
Baire functions 209—211
Banach — Mazur distance 112 120 124
Banach — Stone Theorem 341—342
Banach — Stone theorem for Bochner -spaces 287
Banach — Stone theorem for operator spaces 274 275
BAP (see Approximation property bounded)
Barycentric calculus 28
Basic inequality 340
Basis, subsymmetric 331
Basis, symmetric 304
Basis, unconditional 303
Bergman space 150
Biface 81
Bishop — Phelps theorem 270
Bishop — Phelps — Bollobas theorem 270
Bloch spaces 105 123 151
Blocking technique 242
Boolean algebras of projections 46—47
Borsuk — Dugundji theorem 64
Bounded extension property 14 64
Buhvalov — Lozanovskii theorem 183
C*-algebras and M-embedded spaces 120
C*-algebras, Arens regularity 219
C*-algebras, biduals of 219
C*-algebras, Centralizer of 236
C*-algebras, M-ideals in 234
CAP (see Approximation property compact)
Centralizer and structurally continuous functions 39
Centralizer of -spaces 90
Centralizer of an injective tensor product 288 339
Centralizer of C*-algebras 236
Centralizer of dual spaces 39
Centralizer of G-spaces 88 89
Centralizer of JB*-triples 257
Centralizer of L(X,Y) 264 274
Centralizer of M-embedded spaces 116
Centralizer of the bidual 40 116
Centralizer of unital Banach algebras 221
Centralizer, connection with M-ideals 39
Centralizer, definition 36
Characteristic of a subspace 67 133
Chebyshev subspace 49 52
Cochain complex 236
Cohomology groups 236—239 259—261
Compact abelian groups 189 203—207
Compact operators (see M-ideals of compact operators)
Completely bounded maps 257—259
Convergence in measure 179 202
Convex combinations argument 242 295
Cunningham algebra of -spaces 39
Cunningham algebra of a projective tensor product 285
Cunningham algebra, definition 39
Daugavet’s equation 342
Dauns — Hofmann theorem 39
Density character 126 139
Dirichlet problem 98
Disk algebra and linear extension operators 64
Disk algebra, dual of 158
Disk algebra, extreme functionals on 4
Disk algebra, M-ideals in 4 24 85
Disk algebra, quotient by (see Space C/A)
Douglas algebras 152—153
E(n)-space 99
Essential norm 292
F-projections 46
F. and M. Riesz theorem, abstract 109
F. and M. Riesz theorem, classical 4 190
Finite dimensional decomposition 303
Fourier transform 189
Function algebras M-ideals in 233
Function module 47
G-spaces vs. square Banach spaces 94
G-spaces, Centralizer of 88 89
G-spaces, complex 100
G-spaces, definition 83
G-spaces, extreme functionals on 89
G-spaces, M-ideals in 83
G-spaces, structure topology of 86
Gelfand-Naimark theorem vi
Grade of a pseudoball 50
Grade of an M-ideal 67 98—99
Haar invariant sets 190—192
Hahn — Banach extension operator 135
Hahn — Banach smoothness 10 44 96 125 147
Hahn — Banach smoothness, strong 44
Hankel operator 112
Hardy spaces 104 105 158 170 183 320
Harmonic functions 97
Hausdorff metric 54
HB-subspaces 44 333
Hermitian element 218 219
Hermitian operator 17 36 40 246
Hyperstonean 47 273
Injective tensor product, Centralizer of 288 339
Injective tensor product, definition 265
Injective tensor product, dual space of 265
Injective tensor product, M-ideals in 282—284
Injective tensor product, structure topology of 288
INNER 225
Inner M-ideals in commutative Banach algebras 232
Inner M-ideals in L(X) 243—250
Inner M-ideals in unital Banach algebras 225—232
Inner M-ideals of compact operators 295
Inner M-ideals, characterisation 227
Inner M-ideals, definition 225
Inner multiplier 225
Integral operator 265
Interpolation set 97
Intersection properties of balls (see E(n)-space n-ball n.k.
| Intersection property IP 74
Intersection property IP, relation with proper M-ideals 77 78
IP (see intersection property IP)
JB*-algebras 254—255
JB*-triples 255—257
L-embedded spaces in the dual of an M-embedded, space 116
L-embedded spaces vs. semi L-embedded spaces 200—201
L-embedded spaces, among subspaces of 179—188 195
L-embedded spaces, connection with Riesz sets 191
L-embedded spaces, contain copies of £l 131 170 176
L-embedded spaces, definition 101
L-embedded spaces, duals of M-embedded spaces 102 164 176 188 195
L-embedded spaces, examples 150 158 199
L-embedded spaces, extreme points 166 177
L-embedded spaces, in 6
L-embedded spaces, L-ideals 2
L-embedded spaces, metric projections 165
L-embedded spaces, preduals of 163
L-embedded spaces, property (V*) 131 173
L-embedded spaces, proximinality 165
L-embedded spaces, Radon — Nikodym property 126 176—179 197
L-embedded spaces, stability properties 159—163 199 200
L-embedded spaces, weak sequential completeness 131 169 172
L-projections, definition 1
L-summands in 6
L-summands in a projective tensor product 286
L-summands in biduals (see L-embedded spaces)
L-summands in smooth spaces 6
L-summands in strictly convex spaces 6
L-summands in subspaces of 15
L-summands vs. M-summands 7
L-summands, complementary 2
L-summands, definition 1
Liftings, linear 59 259
Liftings, nonlinear 55 166
Lindenstrauss — Tzafriri theorem 331
Linear extension theorems 64 96—98
Lipschitz projections, onto M-ideals 56
Lipschitz projections, onto semi L-summands 44
Lipschitz selection for 95
Local reflexivity 217 259
Locally uniformly rotund 142
Lorentz spaces 103 105 327
LUR (see Locally uniformly rotund)
M-embedded spaces among -preduals 119
M-embedded spaces among -spaces 134
M-embedded spaces among C*-algebras 120
M-embedded spaces among quotients of C(G) 195
M-embedded spaces and M-ideals of compact operators 291 295
M-embedded spaces, Asplund property 126
M-embedded spaces, centralizer of 116
M-embedded spaces, characterisation 113
M-embedded spaces, contain copies of 131 145
M-embedded spaces, decomposition 119
M-embedded spaces, definition 101
M-embedded spaces, duals of 102 164
M-embedded spaces, duals of among subspaces of 188 195
M-embedded spaces, duals of norming subspaces 125 133
M-embedded spaces, duals of Radon — Nikodym property 126 176 197
M-embedded spaces, duals of weak* topology on the sphere 291 297
M-embedded spaces, examples 105 124 148—151
M-embedded spaces, M-ideals in 116
M-embedded spaces, projectional resolutions of the identity in 140
M-embedded spaces, property (u) 132 213
M-embedded spaces, property (V) 129
M-embedded spaces, Radon — Nikodym property 126 131
M-embedded spaces, renormings 123 124 142 213
M-embedded spaces, shrinking Markusevic basis 142
M-embedded spaces, stability properties 111 112
M-embedded spaces, unique extension property 117
M-embedded spaces, unique preduals 122 163
M-embedded spaces, weakly compactly generated 142
M-ideals and £p-subspaces 318 324
M-ideals and approximation property 295 301 306
M-ideals and Douglas algebras 152—153
M-ideals and M-embedded spaces 291 295
M-ideals and nest algebras 253
M-ideals and renormings 328—332
M-ideals and subsymmetric bases 331
M-ideals and symmetric bases 305
M-ideals and unconditional bases 304
M-ideals in 3
M-ideals in -preduals 81
M-ideals in A(K) 5
M-ideals in an injective tensor product 282—284
M-ideals in biduals (see M-embedded spaces)
M-ideals in C(K,X) 284
M-ideals in C*-algebras 234
M-ideals in commutative Banach algebras 232
M-ideals in function algebras 233
M-ideals in G-spaces 83
M-ideals in JB*-algebras 255
M-ideals in JB*-triples 257
M-ideals in K(X,Y) 285
M-ideals in L(X) 243—250
M-ideals in L(X,C(K)) 275—281
M-ideals in M-embedded spaces 116
M-ideals in quotients of C(K) 16
M-ideals in smooth spaces 6
M-ideals in strictly convex spaces 6
M-ideals in subalgebras of G*-algebras 252
M-ideals in subspaces of C(K) 14—15
M-ideals in the disk algebra 4 24 85
M-ideals in unital Banach algebras 221 224—232
M-ideals inner in commutative Banach algebras 232
M-ideals inner, characterisation 227
M-ideals inner, definition 225
M-ideals of compact operators 289—332
M-ideals vs. algebraic ideals 227 231—234 243 246
M-ideals vs. L-summands 7
M-ideals vs. M-summands 3 65—73
M-ideals, and pseudoballs 69
M-ideals, characterisation by maximal measures 25
M-ideals, characterisation by n-ball property 18
M-ideals, characterisation theorem 299
M-ideals, complete 259
M-ideals, contain copies of 72 78
M-ideals, definition 1
M-ideals, examples 289 302 308 322 327 336
M-ideals, extreme 67 73
M-ideals, grade of 67 98—99
M-ideals, Hahn — Banach smoothness 11
M-ideals, inner 295
M-ideals, intersections of 10 84—85
M-ideals, maximal 276
M-ideals, nontrivial 1
M-ideals, proper 65 284
M-ideals, proximinality 50
M-ideals, real vs. complex 16
M-ideals, relation with the IP 77 78
M-ideals, stability properties 290 301 318
M-ideals, sums of 10
M-ideals, unconditional expansion into elements of 31 303
M-ideals, weak* closed 67 93
M-projections in 3
M-projections in dual spaces 9 39
M-projections, almost 338
M-projections, belong to the Centralizer 36
M-projections, definition 1
M-summands in 3
M-summands in dual spaces 9
M-summands in L(X,Y) 273 274
M-summands in unital Banach algebras 224
M-summands vs. L-summands 7
M-summands vs. M-ideals 3 65—73
M-summands, characterisation by intersection properties of balls 66
M-summands, complementary 2
M-summands, definition 1
MAP (see Approximation property metric)
Maximal measure 25
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