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Singer I. — Bases in Banach spaces I
Singer I. — Bases in Banach spaces I

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Название: Bases in Banach spaces I

Автор: Singer I.

Аннотация:

This monograph attempts to present the results known today on bases in Banach spaces and some unsolved problems concerning them.


Язык: en

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1970

Количество страниц: 341

Добавлена в каталог: 20.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Lambda$ sequence      198
${\gamma_n}$-neighbourhood      106
(M)-convergent      147
A.s.c.f. = associated sequence of coefficient functionals      17 151
Akutowicz, E.      201
Alaoglu, L.      625
Albinus, G.      633
Altman, M.S.      206 629 630 633
Antilinear      9
Approximation property      171
Arsove, M.G.      202 204 206 209 210
Arzela, C.      248 376
Ascoli, G.      623
Auerbach, H.      623
Automorphism      4
Averaging projection      589
Babenko, K.I.      205 629 633 634
Baire, R.      33 34 438 439
Banach — Mazur theorem      2 499
Banach — Steinhaus theorem      348
Banach, S.      2 19 20 24 29 32 116 200 201 202 203 204 207 208 209 349 469 623
Bari, N.K.      208 629 630 633 640
Baric, L.W.      207 209
Base of a cone      320
Basic sequence      27
Basic sequence of type $l_+$      369
Basic sequence, block      66
Basic sequence, unconditional      505
Basis      1 144
Basis $bw^*$-Schauder      153
Basis $\infty$-Besselian      354
Basis $\infty$-Hilbertian      354
Basis $\sigma(E, [f_n])$-uniform      645
Basis (weakly closed)*      301
Basis of type $(al_+)^*$      315
Basis of type $(l_+)^*$      315
Basis of type $(swc_0)^*$      292
Basis of type $(wc_0)^*$      292
Basis of type $al_+$      315
Basis of type $aP^*$      308
Basis of type $P^*$      308
Basis of type $swc_0$      292
Basis of type $s\mathscr{B}$      629
Basis of type $wc_0$      292
Basis of type $а\mathscr{B}$      626
Basis of type $\l_+$      315
Basis of type $\mathscr{B}^*$      626
Basis of type aP      308
Basis of type P      308
Basis problem      2
Basis with a discontinuity of the unconditionally      636
Basis with a simple discontinuity of the unconditionality      636
Basis with respect to $M \subset E^*$      147
Basis, $(F,\{e_n\})$-Besselian      354
Basis, $(f,\{e_n\})$-Hilbertian      354
Basis, $w^*$-Schauder      153
Basis, $w^*$-uniform      645
Basis, $\mathrm{weak}^*$ ($w^*-$)      145
Basis, (b)-Schauder      158
Basis, (e)-Schauder      158
Basis, absolute      625
Basis, absolutely convergent      621
Basis, Besselian      337
Basis, block-universal      388
Basis, bounded      21
Basis, bounded $\mathrm{weak}^*$ ($ = bw^*-$)      145
Basis, bounded weak ( = bw-)      145
Basis, boundedly complete      284
Basis, bw-Schauder      153
Basis, complementably universal      374
Basis, conditional      396
Basis, Haar, of $L^p$([0,l])      16
Basis, Hilbertian      338
Basis, hyperorthogonal      558
Basis, k-boundedly complete      284
Basis, k-shrinking      268
Basis, monotone      214
Basis, natural, of $c_0$, $l^p$      11
Basis, non-absolute      632
Basis, non-monotone      213
Basis, normal      252
Basis, normalized      21
Basis, orthogonal      555
Basis, p-Besselian      354
Basis, p-Hilbertian      354
Basis, perfectly homogeneous      609
Basis, permutatively homogeneous      641
Basis, polynomial      184
Basis, positive      261
Basis, retro-basis      279
Basis, Schauder      152
Basis, Schauder, of C([0,1])      13
Basis, semi-shrinking      625
Basis, shrinking      268
Basis, strict polynomial      184
Basis, strictly co-orthogonal      641
Basis, strictly hyperorthogonal      558
Basis, strictly monotone      214
Basis, strictly orthogonal      555
Basis, subsymmetric      563
Basis, symmetric      574
Basis, T-uniform      644
Basis, unconditional      396
Basis, uniform      622
Basis, unit vector, of $c_0$, $l^p$      11
Basis, universal      373
Basis, w-Schauder      153
Basis, w-uniform      645
Basis, weak (w-)      145
Basis, weakly closed      300
Berkson, E.      208
Bessaga, C.      202 203 204 205 206 207 209 210 623 625 637 638 640 641
Biorthogonal system      23
Biorthogonal system, E-complete      24
Biorthogonal system, irregular      25
Biorthogonal system, regular      25
Biorthogonal system, total      472
Block basic sequence      66
Block perturbation      30
Block subspace      506
Boas, R.P.      205
Bohnenblust, H.F.      208 220 623 644
Bounded $\mathrm{weak}^*$ topology (= $bw^*$-topology)      145
Bounded weak topology ( = bw-topology)      145
Bourbaki, N.      200
Byckov, B.M.      637
Canonical mapping of E into $V^*$, where $V \subset E^*$      114
Canonical mapping of E into E**      113
Canturija, Z.A.      629 630
Cartesian product of an infinity of bases      82
Cartesian product of two bases      29
Cartesian product of two equivalence classes      82
Ceitlin, Ya.M.      638
Characteristic (of a subspace of a conjugate space)      115
Ciesielski, Z.      201
Circled      22
Coefficient functionals      17
Coefficient functionals, associated sequence of      17 151
Compact, conditionally      297
Compact, countably      297
Compact, sequentially      297
Complemented subsequence      373
Complete (sequence)      24
Complete (sequence) of order p      78
Complete (sequence), $\{a_n\}$-complete      78
Complex structure      4
Complexification      5
Condition (A)      217
Cone      320
Cone associated to a basis      320
Cone associated to a biorthogonal system      472
Cone solid      321
Cone, generating      327
Cone, minihedral      473
Cone, normal      328
Cone, regular      479
Conjugate function      344
Coordinate space      131
Darboux, F.      245
Davies, R.O.      212
Davis, P.      205
Davis, W.J.      206 624 642 644
Day, M.M.      200 209 622 623 638 642
Dean, D.W.      644
Dieudonne, J.      200
Disjoint support condition      264
Distance between two basic sequences      207
Distance between two classes of related bases      207
Dixmier, J.      118 149
Domination      68
Domination, affine      79
Domination, permutative      79
Domination, strict      68
Dual (of a sequence space), $\alpha$-dual      526
Dual norm      280
Dual, $\beta$-dual      135
Dual, $\gamma$-dual      131
Dual, $\sigma$-dual      596
Duality properties      112
Duality properties, strong      112
Duality properties, weak      112 151
Duffin, R.J.      206
Dunford, N.      625
Dvoretzky, A.      303 306
Eachus, J.J.      206
Eberlein — Smulian theorem      297
Edelstein, I.      642 643
Edwards, R.E.      204 209 210
Element of best approximation      175
Ellis, H.W.      201
Endomorphism      54
Equivalent bases      68
Equivalent bases, affinely      79
Equivalent bases, permutatively      79
Equivalent sequences      68
Equivalent sequences, fully      69
Equivalent sequences, strictly      68
Equivalent spaces      2
Existence problem      213
Existence problem, restricted      213
Extremal point      321
Extremal subset      321
Ezrohi, I.A.      211
Fan, Ky      205
Fichtengolz, G.      245
Field of scalars      1
Field of scalars, extension of      5
Field of scalars, restriction of      2
Foguel, S.R.      202
Foias, C.      629
Formal expansion      25
Fubini, G.      426
Fullerton, R.E.      628 629 632 638
Fundamental parallelotope of Hilbert      475
Gaposhkin, V.F.      208 624 629 630 633 641
Garling, D. J.H.      643
Gelbaum, B.R.      202 209 210 211 624 629 632 633 640
Gelfand, I.M.      208 211 637 638 640
Gil de Lamadrid, J.      211 640
Goffman, C.      210
Gohberg, I.C.      623 629 630
Gram — Schmidt orthogonalization procedure      24 212 428 431
Gram, J.P.      212 428 431
Grinblium, M.M.      202 203 205 207 208 623 624 638 640
Grober, V.M.      637
Grothendieck, A.      151 170 171 641
Gurarii, V.I.      203 622 623 630 643
Gurevich, L.A.      204 205 208 211 624 638 640
Haar functions      13
Haar system with respect to a basis      598
Hahn — Banach theorem      55 229 272 280 293 297 310 330 440 445 448
Halperin, I.      201
Hardy, G.H.      414
Harsiladze, F.I.      194 195 212
Helly, E.      127 309
Helson, H.      634
Hildebrandt, T.H.      638
Hilding, S.H.      206 208
Holub, J.R.      204 625 626 627 631 636 638 640
Hyperbase of a cone      329
Hyperoctahedron      255
Hyperparallelepiped      255
Inclination      63
Index of a sequence      63
Index of a space      63
Index, unconditional, of a sequence      504
Infinite power (of an equivalence class)      82
Involution      9
Ishii, J.      201
Isomorphic      2
Isomorphically universal space      389
Istraetescu, V.      212
James, R.C.      203 211 622 624 625 628 640 641
Joiner, H.      627
Kaczmarz, S.      203
Kadec, M.I.      203 208 212 623 637 639 640 642 643
Kaplansky, I.      200
Karlin, S.      208 209 623 624 625 629 632 633 637 642 644
KB-lineal      559
Khinchin inequality      425 644
Klee, V.      639
KMR property      157
KMR property for bases      157
KMR property for Schauder bases      157
Koethe, G.      200
Kottman, C.      624
Kozlov, V.Ya.      207 622
Krasnoselskii, M.A.      201 479 623
Krein — Milman — Rutman theorem      98 157 212 249
Krein, M.G.      206 208 623 639
Kwapien, S.      640
Landau, E.      426
Lebesgue, H.      295 301 425 440
length function      16
Levelling length function      16
Levin, A.Yu.      623
Lichnerowicz, A.      200
Limit point      297
Lindenstrauss, J.      625 631 634 638 641 643 644
Linear manifold      329
Linearly independent      50
Linearly independent, $c_0$-linearly independent      356
Linearly independent, $l^2$-linearly independent      347
Linearly independent, $l^p$-linearly independent      356
Linearly independent, $\omega$-linearly independent      50
Linearly independent, finitely      50
Linearly independent, strongly      57
Linearly independent, unconditionally $\omega$-linearly independent      470
Linearly independent,$(F,\{e_n\})$-linearly independent      356
Littlewood, J.      414
Liusternik, L.A.      206 208 211
Locally isomorphic      323
Lorentz, G.G.      630
Lovaglia, A.R.      625
Lozinski, S.M.      194 195 212
Luzin, N.      436
Marcinkiewicz, J.      633
Markus, A.S.      623 629 630
Markushevich, A.I.      57 202 203 205
Matrix norm      507
1 2
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