Singer I. — Bases in Banach spaces II :: Электронная библиотека попечительского совета мехмата МГУ

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Singer I. — Bases in Banach spaces II

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Название: Bases in Banach spaces II

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:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1981

Количество страниц: 880

Добавлена в каталог: 11.12.2011

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

Предметный указатель

Astriction      475
Asymptotically attained      796
Average trace      5 722
B      98
B-orthogonal      838
Bachelis, G.F.      759 805 825 864
Banach space containing uniformly $l^{1}_{n}$       749
Banach space containing uniformly $l^{\infty}_{n}$       745
Banach, S.      111 727 756 760 762 763 766
Bari, N.K.      787
Bartle, R.G.      151
Basic sequence      47
Basic sequence (family) of subspaces      802
Basic sequence of subspaces, Schauder      802
Basic sequence of type $l_{+}$       54
Basic sequence with parentheses      459
Basic sequence with parentheses, w*-Schauder      459
Basic sequence, almost monotone      60
Basic sequence, asymptotically monotone      60
Basic sequence, monotone, normal, etc.      60
Basic sequence, w*-Schauder      64
Basis for a set      559
Basis of a set      559
Basis of a set, unconditional (etc.)      566
Basis with parentheses      450
Basis with parentheses, shrinking      459
Basis with respect to a class of sequences of indices      141
Basis, $(F, \{e_{n}\})$ -Besselian      115
Basis, absolutely convergent      804
Basis, asymptotically monotone      771
Basis, hyperorthogonal      744
Basis, standard conditional (of $c_{0}$ )      142
Basis, unconditionally monotone      811
Benyamini, Y.      738
Berkson, E.      811
Bessaga, C.      63 727 728 730 756 763 767 798 809 812 813 814 819 827 828 867
Best approximation      380
Bibasic system      85
Bibasic system, cofinal (cofinal biorthogonal system)      547 805
Bierstedt, K.-D.      719
Billard, P.      794
Biorthogonal system of subspaces      800
Biorthogonal system, E-complete      183
Biorthogonal system, maximal      183
Biorthogonal system, total      190
Biorthogonal systems associated to a projection basis      812
Biorthogonalization      760
BK-space      189 515
Block basic sequence with respect to a sequence      76
Block sequence      164
Blocking (block Schauder decomposition)      506
Bohnenblust functions      289
Boolean algebra of projections      810
Bounded 2-variation      365
Bows (biorthogonal system in the wide sense)      837
Brace, J.W.      717
Brass, H.      729 753 754
Braun, Ben-Ami      755
Browder, F.E.      791
BS-space      190
Buhvalov, A.V.      721
Butzer, P.L.      785 801
bv      365
Canturija, Z.A.      786 788 790
card M = |M|      5
Casazza, P.G.      748 864
Cesaro basis      350
Cesaro decomposition      501
Cesaro summation method $(C,\ \alpha)$       358
Chadwick, J.J.M.      802 803 805 821 822 823 824 828
CHARACTER      9
Characteristic with respect to a subspace      90
Circled      40
class      141
co Q      741
Coefficient functionals      47 574 582
Coefficient space      779
Commuting $\pi$ -basis      431
Commuting $\pi$ -basis, strict      431
Commuting $\pi^{\infty}_{1}$ -basis      431
Commuting $\pi^{\infty}_{1}$ -basis, strict      431
Commuting $\pi_{\lambda}$ -basis ( $\pi_{\lambda}$ -dual $\pi_{\lambda}$ decomposition)      431 794
Commuting $\pi_{\lambda}$ -basis, strict      431
Commuting approximative basis      313
Commuting approximative basis, shrinking      318
Compact, conditionally weakly      53
Complementary universal      296 720
Cone      560
Cone, generating      568
Cone, minihedral      568
Cone, normal      567
Constant, $\Pi$ -basis      792
Constant, bounded approximation      770
Constant, finite-dimensional decomposition      795
Continual basis      806
Continual basis, Besselian      806
Continual basis, Hilbertian      806
Convex sequence      365
Cooke, R.G.      791
Coordinate operators      515
Coordinate projections      486 622 825
CoType      726
Courage, W.H.      756 761
Crone, L.      765 790
d(a, b)      422
D(E, E)      257
D(z(.))      693
Dacunha-Castelle, D.      721
Dashiell, F.K.      832
Davie, A.M.      721 722 725 726
Davis, W.J.      726 752 756 757 759 761 776 779 805 817 831 832
Dawson, D.F.      785
Day, M.M.      729 730 784 834
de Figueiredo, D.G.      791 819
De la Vallee Poussin means      382
Dean, D.W.      752 761 773 775 779 798 800 817 819
Decomposition (basis of subspaces)      485
Decomposition, bounded weak      800
Decomposition, bounded weak*      800
Decomposition, finite-dimensional      455
Decomposition, Schauder      487
Decomposition, Schauder associated to an integral basis      558
Decomposition, Schauder of type $wc_{0}$       530
Decomposition, Schauder, $(F,\ \{e_{n}\})$ -Besselian      530
Decomposition, Schauder, $(F,\ \{e_{n}\})$ -Hilbertian      531
Decomposition, Schauder, $\infty$ -Besselian      531
Decomposition, Schauder, $\infty$ -Hilbertian      531
Decomposition, Schauder, absolutely convergent      537
Decomposition, Schauder, Besselian      531
Decomposition, Schauder, block p-Besselian      804
Decomposition, Schauder, block p-Hilbertian      804
Decomposition, Schauder, bounded weak      518
Decomposition, Schauder, bounded weak*      518
Decomposition, Schauder, boundedly complete      526
Decomposition, Schauder, conditional      534
Decomposition, Schauder, Hilbertian      531
Decomposition, Schauder, hyperorthogonal      536
Decomposition, Schauder, lattice type      549
Decomposition, Schauder, monotone      522
Decomposition, Schauder, normal      523
Decomposition, Schauder, orthogonal      536
Decomposition, Schauder, p-Besselian      531
Decomposition, Schauder, p-Hilbertian      531
Decomposition, Schauder, shrinking      524
Decomposition, Schauder, unconditional      534
Decomposition, Schauder, weak      518
Decomposition, Schauder, weak*      518
Decomposition, w*-Schauder finite-dimensional      795
Decomposition, weak      518
Decomposition, weak Schauder      518

Decomposition, weak*      518
Decomposition, weak* Schauder      518
Deficient basic sequence      103
Deficient basic sequence, $(F,\ \{e_{n}\})$ -Besselian      116
Deficient basic sequence, monotone, normal, etc.      125
Deficient minimal sequence      121
dens E      577
Density character      577
Diestel, J.      770 829 832 834 856 865
Dieudonne, J.      758 759 831
Distance coefficient      422
Division points      40
Domination, strict      507
Dor, L.E.      728 772 812
Dorembus, L.      812 814 828 829
Drewnowski, L.      857
Dual $\pi$ -basis (Schauder dual operator basis)      429 793
Dual $\pi$ -basis, strict      429
Dual $\pi$ -basis, weak      447
Dual $\pi$ -basis, weak*      447
Dual $\pi^{\infty}_{1}$ -basis (dual $\pi^{\infty}_{1}$ decomposition)      429 793
Dual $\pi_{\lambda}$ -basis (dual $\pi_{\lambda}$ decomposition, dual $\pi_{\lambda}$ system)      429 793
Dual $\pi_{\lambda}$ -basis, strict      429
Dual $\pi_{\lambda}$ -basis, weak      447
Dual $\pi_{\lambda}$ -basis, weak*      447
Dual associated sequence space      765
Dubinsky, E.      804 820
Dunford — Pettis property      497
Dunford, N.      827
Dvoretzky, A.      168 169 757 764
Dyer, J.A.      815 831 832 837 838
Edwards, R.E.      758 759 788 790 791 805 806 807 810 811 815 832
Eggleston, H.G.      793
Ellis, H.W.      819
Enflo, P.      720 721 722 726 750 771 792 808 809
Equivalent bases      209
Equivalent basic sequences      47 209
Equivalent sequences of subspaces, fully      507
Equivalent sequences of subspaces, strictly      507
ER-set (Enflo — Rosenthal set, Schauder basis set)      572 808
ER-set of subspaces (ER-decomposition)      826
ER-set of subspaces, Schauder      826
ER-set, boundedly complete      577
ER-set, shrinking      577
Erdoes, P.      729 756
Ergodic theorem      311
Extended $\lambda$ -approximative basis      609
Extended $\pi$ -basis      611
Extended $\pi^{\infty}_{1}$ -basis      611
Extended $\pi_{\lambda}$ -basis      611
Extended approximative basis      603
Extended biorthogonal system      673
Extended biorthogonal system, E-complete      673
Extended biorthogonal system, maximal      685
Extended biorthogonal system, normal      685
Extended biorthogonal system, norming      831
Extended biorthogonal system, strictly bounded      685
Extended biorthogonal system, total      673
Extended BK-space      685
Extended commuting $\lambda$ -approximative basis      608
Extended commuting $\pi$ -basis      611
Extended commuting $\pi^{\infty}_{1}$ -basis      611
Extended commuting $\pi_{\lambda}$ -basis      611
Extended commuting approximative basis      608
Extended dual $\pi$ -basis      611
Extended dual $\pi^{\infty}_{1}$ -basis      611
Extended dual $\pi_{\lambda}$ -basis      611
Extended generalized biorthogonal system      826
Extended M-basis      691
Extended M-basis, 1-norming      836
Extended M-basis, boundedly complete      716
Extended M-basis, norming      697
Extended M-basis, shrinking      699
Extended resolution of the identity (of $I_{E}$ )      620 821
Extended resolution of the identity, boundedly complete      621
Extended resolution of the identity, monotone      621
Extended resolution of the identity, shrinking      621
Extended unconditional basis (unconditional ER-set, absolute basis of power I, extended basis)      577 809
Extended unconditional basis, hyperorthogonal      579 811
Extended unconditional basis, orthogonal      579
Extended unconditional basis, strictly hyperorthogonal      579
Extended unconditional basis, strictly orthogonal      579
Extended unconditional basis, symmetric      811
Extended unconditional Schauder decomposition (extended unconditional Schauder basis of subspaces, unordered Schauder decomposition, unordered Schauder basis of subspaces)      825
Extended weak $\lambda$ -approximative basis      609
Extended weak $\Pi$ - ( $\pi$ -, $\pi_{\lambda}$ -, dual $\pi$ -, dual $\pi_{\lambda}$ - etc.) basis      617
Extended weak approximative basis      609
Extended weak* $\lambda$ -approximative basis      609
Extended weak* approximative basis      609
Extension of a biorthogonal system      183
Fage, M.K.      798
Feder, M.      860
Fejer, L.      358
Figiel, T.      719 720 721 722 723 724 725 726 738 750 769 770 781 811 864
Finite expansion operator      722
Finite-dimensional $\lambda$ -expansion of the identity (of $I_{E}$ )      289
Finite-dimensional counterpart of the basis problem      767
Finite-dimensional expansion of the identity (of $I_{E}$ )      289
Finite-dimensional expansion of the identity, absolutely convergent      542
Finite-dimensional expansion of the identity, unconditional      309
Finite-dimensional subspace basis property      820
Finitely universal      745
Fleming, D.J.      765 790 794 795 817 821 822 824
Fleming, R.J.      811
Formal expansion      498
Fremlin, D.H.      811 812
Friedland, D.      834
Frink, O., Jr.      760 783 787
Fullerton, R.E.      810 815
Gap      381
Gaposkin, V.F.      760 776 780 784 785 787
Garling, D.J.H.      758 759
Gelbaum, B.R.      727 755 761 766 783 784 786
Generalized basic sequence      206
Generalized basis      189
Generalized basis, almost normal      212
Generalized basis, boundedly complete      216
Generalized basis, normal      212
Generalized basis, quasi-boundedly complete      215
Generalized basis, shrinking      215
Generalized basis, strictly bounded      212
Generalized biorthogonal system      498 800
Generalized biorthogonal system, E-complete      498
Generalized biorthogonal system, total      500
Generalized M-basis      838
Generalized summation basis      341
Generalized summation basis, double      348
Generalized summation basis, multiple      348
Generate      638
Giesy, D.P.      726
Gil de Lamadrid, J.      718
Godun, B.V.      861 862 864 865 866
Goerlich, E.      785
Goes, G.      785
Gohberg, I.C.      753
Gordon, Y.      771 820
Gram — Schmidt orthonormalization procedure      159
Graves, L.M.      151
Grinblium, M.M.      755 756 760 798 801 804
Grothendieck space      497
Grothendieck, A.      717 718 719 753 761 768 769 770 793 818 819 856
Gurarii, N.I.      728
Gurarii, V.I.      728 729 753 754 755 756 761 793 795 807 808 819
Gurevic, L.A.      819
Gutman, S.M.      829 830 835 837
H      9
Haar basis of $l^{2}_{2^{n}}$       248
Hale, D.F.      807
Hall, M., Jr.      724
Hausdorff distance      793

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