Harmand P., Werner D., Werner W. — M-Ideals in Banach Spaces and Banach Algebras :: Электронная библиотека попечительского совета мехмата МГУ

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Harmand P., Werner D., Werner W. — M-Ideals in Banach Spaces and Banach Algebras

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Название: M-Ideals in Banach Spaces and Banach Algebras

Авторы: Harmand P., Werner D., Werner W.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 387

Добавлена в каталог: 15.08.2008

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Предметный указатель

$(M_{p})$ -spaces      306—321 324 336—339
$1\frac{1}{2}$ -ball property      95—96
$c_{0}$ -subspaces      78 131
$C_{\Sigma}$ -spaces vs. $C_{\sigma}$ -spaces      91
$C_{\sigma}$ -spaces, centralizer of      90
$C_{\Sigma}$ -spaces, definition      83
$C_{\sigma}$ -spaces, structure topology of      95
$C_{\Sigma}$ -spaces, ultraproducts of      91
$L^{1}$ -preduals      81—92
$L^{1}$ -preduals and intersection properties of balls      99
$L^{1}$ -preduals and M-embedded spaces      119
$L^{1}$ -preduals, complex      99—100
$L^{p}$ -projections      45
$l^{p}$ -subspaces      131 170 176 208 314 318 324 331
$L^{p}$ -summands      45
-ideals      211—214
-ideals of compact operators      343—344
$\mu$ -closed set      183
$\mu$ -continuous functional      186
$\pi_{1}$ -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 $L^{1}$ -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 $C_{\sigma}$ -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 $L^{1}$ -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 $L^{1}(\mu)$       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 $L^{1}(\mu)$       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 $L^{1}(\mu)$       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 $L^{1}$ -preduals      119
M-embedded spaces among $\mathcal{L}^{\infty}$ -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 $c_{0}$       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 $L^{1}(\mu)$       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 $C_{0}(S)$       3
M-ideals in $L^{1}$ -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 $c_{0}$       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 $C_{0}(S)$       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 $C_{0}(S)$       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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