Fabian M.J., Hajek P., Pelant J. — Functional Analysis and Infinite-Dimensional Geometry :: Электронная библиотека попечительского совета мехмата МГУ

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Fabian M.J., Hajek P., Pelant J. — Functional Analysis and Infinite-Dimensional Geometry

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Название: Functional Analysis and Infinite-Dimensional Geometry

Авторы: Fabian M.J., Hajek P., Pelant J.

Аннотация:

This book introduces the reader to the basic principles of functional analysis theory that are close to nonlinear analysis and topology. The presentation is self-contained, including many folklore results, and the proofs are accessible to students with the usual background in real analysis and topology. Several results are published here for the first time in a monograph. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints. The book is also directed to young researchers in functional analysis and can serve as a reference book, to areas of Banach space.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 451

Добавлена в каталог: 14.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$({B}_{x},w)$       73 75 414 415
$({B}_{x},{w}^{*})$       71—73 319 365 395 409—412
$({B}_{x},||.||)$       2 14
$\epsilon$ -net      30
${S}_{x}$       2
${X}_{c},\;{X}_{c}$       39
Annihilator ${Y}^{\perp}$ and ${Y}_{\perp}$       40 55 58 93 148 149
Banach limit      62
Basis, algebraic      34 191
Basis, Auerbach      139 164
Basis, bimonotone      191
Basis, block      172
Basis, boundedly complete      166—168 182 192
Basis, constant      163 169 182
Basis, equivalent      169—171
Basis, Hamel      see “Basis: algebraic”
Basis, Markushevich      188—190 382 410—412
Basis, Markushevich, shrinking      188 197 369 370
Basis, Markushevich, weakly compact      364
Basis, Markushevich, weakly Lindeloef      411
Basis, monotone      163 191 192
Basis, normalized      163
Basis, orthonormal      18 20 222
Basis, Schauder      161 163 165 303 307
Basis, seminormalized      303
Basis, shrinking      166—168 184 192 260
Basis, summing      165 181
Basis, unconditional      180 181 196 197
Bump      see “”Function”
Cardinality card(A)      23 403
Closure ${\overline{M}}^{{w}^{*}},\;{\overline{M}}^{{w}},\;{\overline{M}}$       64
Compact, Corson      409—412 427 428
Compact, countable      345 399 420
Compact, Eberlein      365 367 388 390—393 409 417 419 420
Compact, scattered      398—401 419 420
Compact, uniform Eberlein      394 395 418 419
Complement      137 138 147—149
Complement, algebraic      137 147
Complement, orthogonal ${F}^{\perp}$       17 18 138
Complement, quasicomplement      377
Constant, basis      163 169 182
Conv(M)      2 22 85 92 104
Convergence, in norm $\rightarrow$       65
Convergence, pointwise      66 68 86
Convergence, weak $\xrightarrow{w}$       65 86 87 105
Convergence, weak star $\xrightarrow{{w}^{*}}$       65 87 105
coordinates      161
Decomposition method      140 174
Density dens(X)      358 359 381 382 397 424
Derivative, Cantor      398
Derivative, directional      241
Derivative, Frechet      241 307
Derivative, Gateaux      241
Dirac measure      48 78
Distance, Banach — Mazur      283
Distributions      116 133
Domain Dom(f)      317
Dual      see “Operator” “Space”
Embedding, canonical $\pi$       63
Epigraph Epi(f)      317
Equality, parallelogram      17 29
Equality, Parseval      20
Equality, polarization      17
Ext(C)      76 78 80 123
Form, bilinear      158
Form, n-linear      313
Form, quadratic      159
Form, symmetric      313
Fourier coefficient/series      19
Function, ${C}^{\infty}$ -smooth      314
Function, ${F}^{k}$ -smooth      314
Function, ${T}^{k}$ -smooth      340
Function, ${w}^{*}$ -differentiable      333 334
Function, bump      314 315 317—319 321 340 342 345 346 424
Function, C-smooth      241
Function, conjugate      321 347
Function, convex      242 247 253 263 265 320
Function, depends on finitely many coordinates      343
Function, Frechet differentiate      241 242 251 253 254 263 320
Function, Gateaux differentiate      241 247 263
Function, inf convolution      265
Function, proper      317
Function, UF      289
Function, UG      289
Functional, biorthogonal      139 164 192
Functional, coordinate      164 171 193 197
Functional, Dirac      48 78
Functional, from X**      69 127
Functional, linear      11 37 38
Functional, Minkowski      42 54
Functional, sublinear      37
Functional, supporting      40 242
Halfspace      64
Homeomorphism      25
Homeomorphism, Lipschitz      331 334 349
Homeomorphism, uniform      133 352 354
Hyperplane      53 76 153
Inequality, Bessel      20
Inequality, Cauchy — Schwarz      3 16
Inequality, Holder      3
Inequality, Khintchine      178
Inequality, Minkowski      4
Inequality, Simons      80
Inequality, triangle      1
Inner product      16
Int(M)      31
James boundary      79 343 344 355
Kernel Ker(T)      11 58 93 208 217
Kronecker ${\delta}_{ij}$       139
Lipschitz      see “”Homeomorphism” “Map”
Local base      107
Map, affine      102
Map, contraction      227 237
Map, differentiation ${D}^{\alpha}$       113 116
Map, fixed point      227
Map, homeomorphism      25
Map, identity ${T}_{x}$       11
Map, Lipschitz      10
Map, nonexpansive      227 237
Map, open      49 50
Map, retract      239
Metric, translation invariant      108
Minkowski      42 54
Modulus, of convexity      285 289
Modulus, of rotundity      285 289
Modulus, of smoothness      288 289
Net      65
Net, Cauchy      109
Norm      1
Norm, ${C}^{1}$ -smooth      241 244
Norm, ${C}^{\infty}$ -smooth      314 344 345 421
Norm, attaining      40 83 102 260 262
Norm, dual      96 245 246 249 280
Norm, equivalent      11 12 25 55
Norm, Frechet differentiate      242—244 249 250 253 254 259 260 267 271 328 367 369
Norm, Gateaux differentiate      242 243 246 247 250 264 275 276 367 382
Norm, LUR (locally uniformly rotund)      248—250 253 271 277 280 281
Norm, operator      see “Operator”
Norm, rotund      246 277 281 305
Norm, strictly convex      246 277 281 305
Norm, UC (uniformly convex)      285 287 290 291 293 294 301 303 305 306 308
Norm, UF (uniformly Frechet)      288—291 293 294 304 306 307
Norm, UG (uniformly Gateaux)      289 395 397
Norm, uniformly smooth      288 290 291 293 294 304 306 307
Norm, UR (uniformly rotund)      285 287 290 291 293 294 301 303 305 306 308
Norm, URED      307 308
Norm, WUR      397
Operator, absolutely summing      372—375
Operator, adjoint T*      217
Operator, bounded      10 11 90

Operator, compact      175 194 203 207—209 215 216 222 223 226 230 232 372
Operator, completely continuous      206 232 375
Operator, Daugavet      310
Operator, dual ${T}^{*}$       51 58 60 90 207 212 371
Operator, eigenspace      214 216
Operator, eigenvalue      214—216 222
Operator, eigenvector      214 221 222
Operator, finite-rank      152 203
Operator, Fredholm      209
Operator, Hilbert — Schmidt      236
Operator, invertible      50 210 211 213
Operator, isometry      11 25 60 90 224
Operator, isomorphism      11 50 60 90 349
Operator, isomorphism into      11 25 59
Operator, norm      11 51 218
Operator, normal      224 226
Operator, on ${c}_{0}$       157 175 176 195 196 233 274 364 365 384
Operator, on ${l}_{p}$       59 90 98 157 175 195 196 232 274
Operator, onto      50 59
Operator, resolvent $\rho(T), R(\lambda)$       211 223
Operator, self-adjoint      217—223
Operator, spectral decomposition      223 226
Operator, spectral radius r(T)      213
Operator, spectrum, $\sigma(T)$       211 212 216 217 219 220 222 234
Operator, spectrum, approximate      310
Operator, strictly singular      175 194 195 235
Operator, unitary      224
Operator, weakly compact      370—372 383
Partition of unity      328
Point, ${w}^{*}$ -strongly exposed      278
Point, cluster      65
Point, diametral      274
Point, exposed      255 276
Point, extreme      76 98 121 276
Point, strongly exposed      255 256 262 277
Polar, ${A}^{0}$ and ${A}_{0}$       118 133
Polarization identity      17
Polynomial      313
PRI      359 382 383
Projection      137 147
Projection, canonical ${P}_{n}$       161 163 165 260
Projection, Dixmier's      148
Projection, orthogonal      225
Property, approximation      192 205
Property, Banach — Saks      89
Property, C      405—407 410 411
Property, CCC      391 392 401
Property, drop      272
Property, Dunford — Pettis      375—377
Property, Grothendieck      195 383
Property, Heine — Borel      114
Property, Kadec — Klee      280 415
Property, lifting      141
Property, Mazur      383
Property, Schur      146 156
Property, three-space      24 97 405 408
Property, w*-Kadec — Klee      280
Rademacher functions ${r}_{n}$       177
Seminorm      37 54
Sequence, basic      169 170
Sequence, basic, equivalent      169—171
Sequence, basic, unconditional      181
Sequence, block basic      172 173
Sequence, bounded      6
Sequence, Cauchy      6
Sequence, weakly Cauchy      145
Series, absolutely convergent      8 27 373
Series, unconditionally convergent      27 186 301 373
Set, balanced      108
Set, bounded      10 69 110
Set, closed      70 118
Set, compact      32 345 387 389 393
Set, convex      22 32 70 118 256 259 326
Set, convex, w-closed      70 118
Set, convex, w-compact      84 279
Set, countably compact      128 130 387
Set, cozero      393
Set, dense      14
Set, fragmented      417
Set, generates space      357
Set, index      65
Set, norming      see “Subspace”
Set, orthonormal      18
Set, point-finite      393
Set, pointwise bounded      68
Set, polar      see “Polar ${A}^{0}$ and ${A}_{0}$ ”
Set, relatively w-compact      128 371
Set, saturated family      119
Set, separated      30 54
Set, separating      93 134
Set, sequentially closed      127
Set, sequentially compact      85 128 130 387 419
Set, totally bounded      110
Set, w*-closed      125 189
Set, w*-compact      92 104 11& 382
Set, w-compact      74 84 85 130 255 258 367 387 418
Slice      77
Space, $C[0,{w}_{1}]$       406 426—428
Space, ${(\sum{l}_{\infty}^{n})}_{2}$       103 193 291 294
Space, ${C}^{n}[0,1]$       24 154
Space, ${C}^{\infty}[0,1]$       133
Space, ${c}_{00}$       6
Space, ${c}_{00}(\Gamma)$       7
Space, ${c}_{0}$       6 14 24 31 44 55 60 74 89 97 99 103 142 143 153—157 164 173 174 180 182 185—187 193 195 205 233 267 269 274 276 280 291 306 331 343 345 355 358 375 377 380 381 383 401 415 421
Space, ${c}_{0}(\Gamma)$       7 45 56 307 358 364 365 378 381 384 394
Space, ${l}_{1}$       44 55 56 88 98 103 140 141 146 155 157 184 185 187 196 232 268 274 306 336 356 375 415
Space, ${l}_{1}(\Gamma)$       56 156 267 358 367 400
Space, ${L}_{1}[0,1]$       22 47 99 183 276 358 385
Space, ${L}_{2}$       15 20 21 31 88 89 98 155 177 193—195 233 306 353 384 385
Space, ${L}_{2}[0,1]$       21 206
Space, ${L}_{p}$       4—6 14 22 23 31 35 45 74 97 131 153 158 159 164 173—175 180 193 195 205 306 336 341 342 385
Space, ${l}_{p}(\Gamma)$       7 45 56 155 195 347
Space, ${L}_{p}(\mu)$       10 286 290
Space, ${L}_{p}[0,1]$       8 15 22 23 45 74 112 154 177 180 193 268 302
Space, ${l}_{\infty}$       3 6 14 15 22—24 44 62 88 95 99 141—143 155 156 187 189 190 194 196 268 346 347 358 377 380 382—384 424
Space, ${l}_{\infty}(\Gamma)$       7 155 378
Space, ${L}_{\infty}[0,1]$       10 15 22 47 99 194 268
Space, ${l}_{\infty}^{n}$       306
Space, ${\mathcal B}(X)$       11
Space, ${\mathcal B}(X,Y)$       414 415
Space, ${\mathcal B}({l}_{2})$       15 233 235
Space, ${\mathcal C}(K)$       3 48 60 72 78 79 99 345 376 387 389 392 394 395 400 401 420 421
Space, ${\mathcal C}(\Omega)$       113
Space, ${\mathcal C}^{\infty}(\Omega)$       113
Space, ${\mathcal D}$       408
Space, ${\mathcal D}'(\Omega)$       see “Distributions”
Space, ${\mathcal D}(\Omega)$       114
Space, ${\mathcal F}(X,Y)$       203 205
Space, ${\mathcal K}(X,Y)$       203 205
Space, (co)type      30 306
Space, angelic      129 130 365 427
Space, Asplund      254 318 397 400
Space, Banach space      1 8
Space, C      6 14 56 99 100 153 154
Space, complete      109 132
Space, complex      39
Space, countable tightness      129
Space, C[0,1]      2 15 47 48 60 74 89 99 144 145 153 164 192 193 195 240 267 273 274 276 288 310 376 377 385
Space, direct sum $X \oplus Y$       11 138 149
Space, direct sum ${(\sum{X}_{n})}_{p}$       56 271 306 381
Space, direct sum ${X \oplus Y)}_{p}$       13 149
Space, dual ${E}^{*}$       111
Space, dual ${E}^{\#}$       117
Space, dual ${X}^{*}$       38 41 167 253
Space, dual second ${X}^{**}$       63
Space, finite-dimensional      12 31 52 66 109 111 263 264 305 306 334
Space, finitely representable      291 293 306 333
Space, fragmented      417
Space, Frechet      108 129
Space, generated by K      357

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