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.

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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

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Предметный указатель

Space, Hilbert      17 20 30 48 140 196 267 277 293 333 340 355
Space, homeomorphic      25 199 337 351 353
Space, infinite-dimensional      14 52 373
Space, injective      142 154
Space, isometric      11
Space, isomorphic      11 307
Space, James      7 185 198
Space, James tree JT      199
Space, Lindeloef      404
Space, Lipschitz equivalent      331 333
Space, locally convex      108
Space, metric      145 233 331 365 418 420
Space, metrizable      71 72 110 390 391 393 399 421 428
Space, normable      108 111
Space, normed      1
Space, Polish      414
Space, pseudocompact      412
Space, quotient X/Y      12 41 96 138 271 306
Space, real      39
Space, reflexive      74 75 84 97 136 168 185 189 244 276 278 291 295 337 357 367 370 372 376 377 384
Space, saturated      343 345 401
Space, second dual X**      69 82 167 275 291
Space, separable      14 26 41 55 71—73 75 82 94 95 140—142 144 182 184 190 197 244 247 248 250 251 253 256 275 280 308 314 328—330 337 345 348 353 357 377 391 410 412 425 428
Space, sequentially compact      85
Space, sequentially complete      196
Space, Sobolev ${W}_{p}^{k}[0,1]$       133
Space, superreflexive      294 303 307 315 328 333
Space, topological vector      107
Space, totally incomparable      175 192
Space, Tsirelson T      311
Space, uniformly homeomorphic      133
Space, WCD      383
Space, WCG      357—359 364—367 369 377 379—383 392 405 408 409 418 428
Space, weak Asplund      248
Space, weakly Lindeloef      404 405 408—411
Span(M)      2 22
Subdifferential      321
Subdifferential, Frechet      320 321
subspace      2 41 75
Subspace, affine      76
Subspace, complemented      137—139 142 147—149 152 350 376 377
Subspace, finite-dimensional      13 109 139
Subspace, invariant      215 221 230 237
Subspace, norming      93 134 193 197 276
Subspace, proper      13
Subspace, quasicomplemented      377 379
Superdifferential      320
Support supp(f)      114 328
Support supp(x)      5
System, biorthogonal      139
Theorem, ${c}_{0}$ complementation      142 143
Theorem, ${l}_{1}$ lifting      141
Theorem, ${l}_{\infty}$ injective      142
Theorem, Alaoglu      71 118
Theorem, almost block subspace      173
Theorem, approximation      329
Theorem, Auerbach      139
Theorem, Banach contraction      227
Theorem, Banach — Dieudonne      125
Theorem, Banach — Mazur      144
Theorem, Banach — Steinhaus      68 69
Theorem, Banach — Stone      79
Theorem, basic sequence      169 170 181
Theorem, Bessaga — Pelczynski      173 186
Theorem, bipolar      119
Theorem, Bishop — Phelps      83
Theorem, Brouwer      229
Theorem, Caratheodory      121
Theorem, Cauchy — Schwarz      3 16
Theorem, Choquet lemma      77

Theorem, Choquet representation      123
Theorem, closed graph      51 57
Theorem, DFJP      366 371
Theorem, dual representation      44 45 47 4
Theorem, Dvoretzky      291
Theorem, Dvoretzky — Rogers      373
Theorem, Eberlein — Smulian      85 128 130
Theorem, extension      40 188 273
Theorem, Fredholm alternative      209
Theorem, Gelfand      213
Theorem, Goldstine      73
Theorem, Gorelik principle      353
Theorem, Hahn — Banach      37 40
Theorem, Helly      33 92
Theorem, Hilbert space is ${l}_{2}$       20
Theorem, Holder inequality      3
Theorem, invariant subspaces      230
Theorem, James      84 168 185
Theorem, Josefson — Nissenzweig      88
Theorem, Kadec      244 248 250 301
Theorem, Kaplansky      129
Theorem, Khintchine      177
Theorem, Korovkin      240
Theorem, Krein      85
Theorem, Krein — Milman      76 101
Theorem, local reflexivity      291 292
Theorem, Mackey et al.      120
Theorem, Markov — Kakutani      228 238
Theorem, Mazur      70 118 422
Theorem, Milman      78
Theorem, Minkowski inequality      4
Theorem, norm attained      40 83 262
Theorem, open mapping      50 57
Theorem, perturbation of basis      171
Theorem, Pietsch factorization      374
Theorem, Pitt      175
Theorem, Ramsey      423
Theorem, Riesz lemma      13
Theorem, root lemma      423
Theorem, Schauder      207 229 230
Theorem, Schur      146
Theorem, selection principle      173
Theorem, separable reduction      254
Theorem, separable spaces in ${l}_{1}$       140
Theorem, separable spaces in ${l}_{\infty}$       142
Theorem, separable spaces in C[0,1]      144
Theorem, separation      41 43 69 70 80 117 330
Theorem, Simons's inequality      80
Theorem, Smulian lemma      243
Theorem, Sobczyk      142
Theorem, spectral decomposition      223 226
Theorem, subspaces of ${l}_{p}$       174
Theorem, uniform boundedness      68 69
Theorem, variational principle      83 317 326 327
Topology, $\sigma(E,F)$       117
Topology, locally convex      108
Topology, Mackey      120 121
Topology, metrizable      71 110 135 417
Topology, norm      66 121
Topology, weak $\omega$       64 96 129 391
Topology, weak star ${\omega}^{*}$       64 71
TREE      199 294 295 308 309
Unit ball ${B}_{x}$       2
Unit sphere ${S}_{x}$       2
Variational Principle      83 317 326 327
Vector, cyclic      237
Vector, fixed point      227
Vector, orthogonal      17 225 276
Vector, standard unit      164
Weight w(T)      424

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