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| Dineen S. — Complex Analysis of Infinite Dimensional Spaces |
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| Предметный указатель |
Holomorphic function of uniformly bounded type 165 228 422
Holomorphic germs 191 210 239 276 288 294 310 315 317 338 389 464 466 469 472 477
Holomorphic Hahn — Banach theorem 472
Holomorphic hull 353
Holomorphic mapping 152
Holomorphic mapping, Asplund 481
Holomorphic mapping, bounding 481
Holomorphic mapping, compact 139 481
Holomorphic mapping, limited 481
Holomorphic mapping, weakly compact 481
Holomorphically barrelled space 235 462 465
Holomorphically convex domain 168 186 324 340 353 355 358 373 389 394 403
Holomorphically infrabarrelled 235
Holomorphically Mackey space 235 465
Holomorphically separated domain 346 354 381
Holomorphy type 76 135
Holomorphy, envelope of 168 236 316 337 338 384 385 388 396 398 463 477
Holomorphy, envelope of bounded 428
Homomorphism 350 388
Homomorphism, bounded 340
Hyperplane 442 453
Hypoanalytic function 159 204 221 294
Hypocontinuous mapping 97 330
Inductive dual 23 30 183 216
Inductive limit 30 155 170 210 222 276 290 333 341 458 463 466 476
Inductive limit, countable 25 27 277
Inductive limit, regular 171 281 291 310 330 388 391 439 469
Inductive limit, strict 28 130 137 223 311 464 469 471
Inductive topology 23 78
Infrabarrelled space 97 222 290 435 465
Injective Banach space 117
Injective tensor product 102 267
Injective topology 102
Integral domination theorem 458
Integral polynomial 105 136 439
Interpolation sequence 478
Isomorphism 337
JB* triple system 51 79
Joint continuity 417
Josefson — Nissenzweig Theorem 157 234
k-dominating cover 223
k-space 132 282 323 330 331 458
kernels 450
Koethe matrix 134 257 265 286 460 470
Koethe sequence space 257 311 331
LB space 239
Lebesgue dominated convergence theorem 145
length function 363
Levi problem 76 174 236 300 323 373 384 389
LF space 459
Lifting 131 444 456 469
Limit, inductive 30 155 170 210 222 276 290 333 341 458 463 466 476
Limit, iterated 60
Limit, joint 60
Limit, projective 17 200 210 388
Limit, surjective 28 163 236 387 449 455 462 478
Limited holomorphic mapping 481
Limited sequence 459
Limited set 141 224 234 279 479
Lindeloef space 71 130 163 372 379 395 402 463
Linear extension operator 58 418
Linearization 3 186 239 391
Liouville's theorem 160 178 235
Lip 1 function 468
Local coordinates 333
Local reflexivity 46 54 55 60 80 412
Local theory 46 187
Local uniform convergence 252
Local weak continuity 255
Localized topology 282
Locally bounded function 15 18
Locally bounded set 15 18 24 27 28 30 67 99 153 171 173 181 182 222 288 293 448
Locally connected set 386
Locally m-convex algebra 223 237 340 370 386 424 457
Loose rank 140
Lower q estimate 121 123 139 455
Lusin measurable function 108
M-ideal 480
m-regular space 443
Mackey convergence criterion 221 239
Mackey convergence criterion, strict 137 464
Mackey null-sequence 226
Mackey space 227 466
Mackey topology 99
Mackey — Arens theorem 183
Mapping, biholoinorphic 50
Mapping, bilinear 2 32 443
Mapping, compact linear 83 88 90 450
Mapping, diagonal 4 55 206
Mapping, hypocontinuous 97 330
Mapping, multilinear 3 6
Mapping, n-linear 2 6 12
Mapping, nuclear 83 135
Mapping, symmetric 416
Mapping, symmetric multilinear 6
Mapping, weakly compact 70 415 440 481
Mapping, weakly continuous 427 444
Markov's inequality 453
Maximum modulus theorem 12 254
Metric approximation property 80 90 134 239 467
Metrically holomorphically convex domain 478
Michael problem 340 396
Minkowski functional 14
Modular hull 202
Modularly decreasing set 202
Monomial 42 145 147 205 254 291 309—311 447 465 473
Monomial basis 124 205 208 249 251 253 304
Monomial expansion 74 148 233 247 274 304 406 422 461
Monomial Theorem 35 43
Monomial, length of 147
Monomial, modulus of 147
Monomial, support of 147
Monotone basis 124 251
Monotone decomposition 189 256 259
Montel space 27 100 258 308 312 459
Montel's theorem 22 183 186 330
Morera's theorem 232
Morphism 337
Multilinear mapping 3 6
Multiplicative function 415 418
Multiplicative functional 168 340 343 379 381 415 424 427
Multiplicative polar 202
n-homogeneous polynomial 4 12
n-linear mapping 2 6 12
Nachbin topology 78 169 463
Nachbin — Shirota Theorem 462
Natural bidual 58
Nicodemi operator 481
Nuclear bornology 240
Nuclear germs 295 312
Nuclear mapping 83 134
Nuclear polynomial 91 106 136 295 457 480
Nuclear space 175 205 207 240 308 318 421 478
Nuclear space, A 206 227 241 290 310 466
Nuclear space, fully 74 97 136 202 231 241 247 287 293 294 300 309 316 386 405
Nuclear type 295
Numerical radius 141
Oka — Weil Approximation Theorem 324 378 382 396 478
Operator ideal 136 242
Operator,  366 395
Operator, compact 83 88 90 450
Operator, convolution 135 297 441 445
Operator, diagonal 84
Operator, Nicodemi 481
Operator, symmetrization 6 29 414
Operator, translation 441
Orlicz space 139 468
Patil's Problem 478
Pietsch conjecture 320
Pietsch integrable function 108
| Plurisubharmonic function 352 403 438 447 468
Plurisubharmonic hull 353
Point evaluation 29 183 426 440
Point of ambiguity 326
Point, exposed 140
Point, extreme 140
polar 39
Polar set 403 438 441 479 483
Polar, multiplicative 202
Polarization Constant 45 79 175 452
Polarization formula 8 21 29 44 46 76 88 95 110 180 181
Polarization Inequality 10 60 76 432 449
Polydisc 74 202 226 230 241 258 286 290 386 409
Polynomial 4 74
Polynomial Dunford — Pettis property 451 472
Polynomial Extension Property 54 57 70 79 451
Polynomial, (r, s)-summing 458
Polynomial, 2-homogeneous 4 5 71 100 134 173 214 308 452
Polynomial, approximable 85 427
Polynomial, compact 68 88 118 137
Polynomial, extendible 439 480
Polynomial, extremal 45 48 450
Polynomial, finite rank 84 90
Polynomial, finite type 42 138 455
Polynomial, hypocontinuous 98
Polynomial, integral 105 136 439
Polynomial, K-bounded 458
Polynomial, n-homogeneous 4 12
Polynomial, nuclear 91 106 136 295 457 480
Polynomial, separately continuous 68 223
Polynomial, separating 137
Polynomial, weakly compact 70 138
Polynomial, weakly continuous 65 70
Polynomial, weakly sequentially continuous 113 116 133 137 274
Polynomially convex domain 235 316 384 386 388 394
Polynomially null sequence 452
Ported topology 23 78 169 463
Power series space 228 409 467
Power series space of finite type 267
Power series space of infinite type 266
Predual 29 38 186 238 239 294 473
Primary space 470
Prime space 41
Principle of local reflexivity 46 54 55 60 80 412
Probleme des topologies 32
PRODUCT 416
Product formula 473
Projection 6 36 38 50 53 55 220 320 333 360 451
Projective description 169 201 276 279
Projective limit 17 200 210 388
Projective limit, reduced 71 452
Projective system 17
Projective tensor product 29 32 125
Projective topology 19 33 41 103
Property ( ) 472
Property ( ) 409 443 472 479
Pseudo-convex completion 443
Pseudo-convex domain 168 233 319 324 340 353 356 366 376 381 383 387 392 403 404 439
PSH()-convex domain 355 377
PSH-convex domain 353 395
Q-reflexive space 125 129 140 435 445 455
Quadratic form 74 230
Quantum field theory 241
Quasi-barrelled space 97
Quasi-complete space 22 215 344
Quasi-local theory 187
Quasi-normable space 131 217 226 239 242 317 390 456 463 464
Quasi-reflexive space 124
Quojection 162 222 236 387 390 392 463
Quojection, twisted 162 471
Rademacher functions 116 138
Radius of boundedness 220 461 468
Radius of uniform convergence 220 461 468
Radon — Nikodym property 107 111 112 124 128 136 309 455
Radon — Nikodym Property, local 137
Ramsey theory 139
random matrix 321
Random variables 8 48
Random variables, independent 63
Rapidly decreasing sequence 180 265
Real analytic function 450
Reasonable norm 450
Reflexive A-nuclear space 207
Reflexive nuclear space 270
Reflexive space 27 113 254 270 275 442
Regular Arens 415 417 424
Regular Banach space 415
Regular inductive limit 171 281 291 310 330 388 391 439 469
Regular symmetrically 424
Reinhardt domain 387 476
Representing measure 166
Reverse polynomial inequalities 453
Riemann domain 237 323 333 343 391 398 430 434 444
Riemann domain, finitely sheeted 389
Riemann domain, holomorphically separated 346
Riemann domain, one-sheeted 334
Riemann domain, pseudo-convex 353
Riemann domain, univalent 334
Riemann surface 334
Riesz representation theorem 61 75 104 166
Rosenthal's  Theorem 116 272 456
Runge approximation theorem 478
Runge property 390
Scattered set 133
Schauder basis 42 139 189 201 205 246 249 252 254 271 287 311 318 360 366 395 459 465 471 478
Schauder decomposition 188 224 239 245 250 257 262
Schur property 114 118 139 141 459
Schwartz space 218 242 258 310 438 463
Second countable space 372
Section 334
Self-adjoint operator 450
Semi-group 434
Semi-montel space 22 219 281
Semi-norm, lower semi-continuous 27 167
Semi-norm, monotone 261
Semi-reflexive space 27 97 226 271
Separately continuous polynomial 68 223
Separately holomorphic function 144 154 165 221 233 461
Separating polynomial 138
Sequence space 201 257 311 331
Sequence, basic 118 123 251 273 309 315
Sequence, interpolating 239
Sequence, Mackey-null 226
Sequence, polynomially-null 452
Sequence, rapidly decreasing 180 265
Sequence, very strongly convergent 177 214 224 312 388 464 476
Sequence, weakly null 114 118 124 139 459
Sequence, weakly summable 130 458
Set, absorbing 27
Set, ambiguity 326
Set, analytic 441 482
Set, bounded 18 21 31 33
Set, bounding 141 157 166 172 234 298 309 311 373 380 400 403 412 419 443 461 462 468 471 479
Set, compact non-polar 405 409
Set, control 404 443
Set, determining 180 225 312 439 461 465
Set, dispersed 133
Set, equicontinuous 15 18 27 30 183 288 296
Set, limited 141 224 234 279 479
Set, locally bounded 15 18 24 27 28 30 67 99 153 171 173 181 182 222 288 293 448
Set, locally connected 386
Set, modularly decreasing 202
Set, polar 403 438 441 479 483
Set, scattered 133
Set, strictly polar 403
Set, uniformly polar 438
Set, weakly compact 416 466
Sheaf topology 390
Shrinking basis 124 247 252 310 314 315
Shrinking decomposition 196 255 273 311 465
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