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

Holub, J.R.      761
Huff, R.E.      834
Hypercomplete (overfilling) sequence      58 279
Hyperparallelepiped      420
i-basis      815
Index of a basis      49
Integral basis      551
Integral basis, Schauder      552
Integral basis, shrinking, boundedly complete, unconditional, etc.      558
Integral basis, strongly unconditional      601
James, R.C.      726 727 757 809
Jamison, J.E.      811
Jessup, P.      765 790
John, F.      767
John, K.      814 828 829 830 832 833 834 835 836 837 866
Johnson, G.W.      856
Johnson, W.B.      719 720 722 723 726 738 750 751 752 756 757 759 760 761 765 767 768 769 770 772 773 775 776 779 780 786 788 790 791 792 793 794 795 796 798 801 804 811 817 818 819 831 832 835 836 837 856 861 864
Josephson, B.      751
Julia, G.      758
K      150
Kaczmarz, S.      758 760 831
Kadec, M.I.      63 728 729 730 753 756 758 760 761 766 769 776 780 784 795 813 858 861 864 866
Kadec, V.M.      858
Kahane, J.-P.      725
Kakutani, S.      759
Kalton, N.J.      798 811 866
Kaplan, S.      837 838
Karlin, S.      752
Kato, T.      753
Keselman, G.M.      806
KL-near      103
Klee, V.      717 729 755 795
Kober, H.A.      802
Koethe, G.      724
Kokilasvili, V.M.      787
Kozlov, V.Ya.      783 784 786
Krein — Milman — Rutman theorem      106
Krein, M.G.      61
Kruse, A.      759
Kuehner, D.G.      819
Kwapien, S.      721 723 724 725 726 856
L(E, E)      1
L-basis (left Cauchy integral basis)      815
Labuda, I.      857
Lacey, E.      751
Lacunary sequence (in the sense of Hadamard)      141 787
Lazar, A.J.      729 793
Legendre polynomials      787
Lewin, S.      760 780
Lewis, D.R.      771 820
Lifting      172 862
lin M      219
Lin, Bor-Luh      748 752 761 864
Lindenstrauss space      793
Lindenstrauss, J.      721 727 738 750 751 766 769 771 773 776 791 792 793 804 809 810 817 818 819 827 828 829 832 833 834 835 836 856 865
Linearly independent sequence of subspaces, finitely      501
Linearly independent sequence, finitely      150
Liokumovic, V.I.      728
Lipecki, Z.      857
Ljance, B.E.      806
Local basis structure      820
Local problem of existence of operational bases      779
Local unconditional structure      810 820
Locally uniformly convex      704
Lohman, R.H.      864
Long sequence      643
Lorch, E.R.      759 808 809 810 827 829
Lyubich, Yu.I.      729
M-basic sequence      227
M-basic sequence, shrinking, etc.      252
M-basis (Markusevic basis, basis in the wide sense)      219 760
M-basis of a normed linear space      219
M-basis, $\Phi_{T}$ -Besselian      786
M-basis, finitely series summable      763
M-basis, k-series summable      763
M-basis, normal      251
M-basis, norming      225
M-basis, series summable      266
M-basis, strictly bounded, etc.      246
M-basis, strong (1-series summable)      242 762
M-basis, strongly series summable      386
M-decomposition (Markusevic decomposition, complete biorthogonal decomposition)      537 805
Macaev, V.I.      755
Mackey, G.W.      760 761
Maddaus, I.      766 772 805
Markus, A.S.      753 798 801
Markusevic, A.I.      755 758 760 832
Marti, J.T.      799 801 809 810 811
Masani, P.      816 817
Matrix, consistent (Toeplitz matrix, permanent summation method)      349
Matrix, consistent corresponding to the convergence with respect to given indices      380 451
Matrix, semi-consistent      783
Matrix, summability (summation matrix)      386 788
Matrix, triangular      350
Maurey, B.      727 730 737
Mazur, S.      718 727 728 730 755 756 798
McArthur, C.W.      798 799 800 801 802 803 804 805 825
McGivney, R.J.      765
Meletidi, M.A.      753 754
Menihes, L.D.      865
Mensov, D.E.      758
Mertens, H.J.      785
Metric homomorphism      71
Michael, E.      791 792 793 819
Milman, D.P.      760
Milman, V.D.      728 729 738 753 754 758 760 761 765 771
Minimal sequence of subspaces      501
Minimal sequence of type $l_{+}$       180
Minimal sequence of type P      182
Minimal sequence of type P*      182
Minimal sequence, $\{\gamma_{n}\}$ -stable (symmetrically stable)      124 753
Minimal sequence, *-semi-bounded      166
Minimal sequence, almost normal      170
Minimal sequence, deficient $\{\gamma_{n}\}$ -stable (symmetrically deficient stable)      124 753
Minimal sequence, maximal      162
Minimal sequence, monotone      166
Minimal sequence, normal      166
Minimal sequence, normalized      166
Minimal sequence, quasi-boundedly complete      175
Minimal sequence, semi-bounded      166
Minimal sequence, shrinking      175
Minimal sequence, strictly bounded      166
Minimal sequence, strongly boundedly complete      175
Minimal sequence, uniformly      142
Minkowski functional      744
Morris, P.      834
Multiplier of an operator      802
Multiplier with respect to a generalized biorthogonal system      500
Murray, F.J.      752
N'(n)      381
N(E, E)      258
Nagumo, M.      717
Nagy, B.-Sz.      827
Nakamura, M.      759
Near, weakly quadratically      103
Nearly isometric      422
Nessel, R.J.      785 801
Net space      824
Nissenzweig, A.      751
Non-approaching      755
Norm of a basis      49
Norm of a quasi-basis      284
Nuclear mapping      258
Nuclear norm      258
Odell, E.      804
Olevskii, A.M.      763
Oostenbrink, W.      770
Opening      533
Operational basis (operatorial basis, operator basis)      325 776
Operational basis, double      348

Operational basis, multiple      348
Operational basis, non-linear      330
Operational basis, unconditional      336
Order of growth      787
Order topology      580
Ordinal resolution of the identity (of $I_{E}$ , of type $\vartheta + 1$ )      626
Ordinal resolution of the identity, boundedly complete      629
Ordinal resolution of the identity, monotone      629
Ordinal resolution of the identity, shrinking      629
Orthogonally scattered measure      816
Orthogonally scattered measure basis (differential basis)      816
Oskolkov, K.I.      787
Ovsepian, R.I.      757 763
P(X)      726
Paley, R.E.A.C.      572
Partial integral operators      556
Partial sum operators associated to a generalized biorthogonal system      498
Partial sum operators associated to a quasi-basis      282
Partial sum operators associated to a Schauder decomposition      498
Partial sum operators associated to a transfinite basis      586
Partial sum operators associated to a transfinite Schauder decomposition      624
Partial sum operators associated to an ER-set      575
Partial sum operators associated to an extended generalized biorthogonal system      826
Partial sum operators associated to an extended unconditional basis      579
Partial sum operators associated to an extended unconditional Schauder basis of subspaces      825
Peaked partition of unity      614
Peaked partition subspace      614
Pelczynski, A.      63 720 721 724 727 728 729 730 737 751 756 757 759 761 762 763 764 767 768 769 771 772 791 793 794 795 798 803 804 805 809 810 817 818 819 820 867
Petersen, L.V.      856
Petryshin, W.V.      791
Petunin, Yu.I.      865
Phelps, R.R.      834
Phillips, R.S.      196 717 766 817 819
Pietsch, A.      802 856
Pisier, G.      727
Plicko, A.N.      756 763 764 831 833 860 861 865
Polynomial of best approximation      188
Principle of local reflexivity      773 796
Projection basis      812
Property $\pi_{\lambda}$       791
Property (u)      809
Property of instability of incompleteness      755
Pseudo-basic sequence      152
Pseudo-basis      150
Pseudo-basis, unconditional      150
Pseudo-decomposition      538
Ptak, V.      758
Pujara, L.R.      820
PW-near      792
q(X)      726
Quasi-basis      278 755
Quasi-basis, monotone      310
Quasi-basis, non-linear      279
Quasi-basis, unconditional      308 539
Quasi-block      738
Quasi-complement      230
Quasi-complementary subspaces      230
Quasi-decomposition      539
Quasi-decomposition, absolutely convergent (absolute Schauder)      542 804
Quasi-decomposition, finite-dimensional      541
Quasi-decomposition, unconditional      539
Quasi-reflexive      776
Quasi-similar biorthogonal systems      211
Quasi-similar generalized bases      211
r(V)      55
Rademacher functions      10
Radon — Nikodym property      770
Reif, J.      814 829 833
Resolution (Schauder resolution) of the identity (of $I_{E}$ )      499
Retherford, J.R.      761 785 799 800 802 803
Richmond, J.B.      803
Riedrich, T.      717
Riesz, F.      827
Riesz, M.      358
Rosenthal, H.P.      728 730 737 748 750 751 759 767 768 769 773 775 791 792 795 796 798 804 808 809 817 818 819 820 825 833 834
Rothman, S.      803
Ruckle, W.H.      760 761 762 763 788 790 794 795 799 800 801 802 803 817 824 825
Russo, J.P.      803
Rutowitz, D.      767
Ryll, J.      819
Salem, R.      725
Samuel, C.      866
Sanders, B.L.      798 799 800 803
Saphar, P.      860
Saxon, S.A.      751
Schatten, R.      766 770
Schwartz, J.T.      827
Section, n-th      190
Seever, G.L.      759
Semadeni, Z.      819
Semi-basis      153 755
Semi-orthogonal      828
Series space of a biorthogonal system      259
Shapiro, J.H.      798
Shelah, S.      861
Silverman — Toeplitz theorem      783
Similar biorthogonal systems      209
Similar generalized bases      209
Smith, K.T.      766
Smooth      659
Snyder, A.K.      762
Sobczyk decomposition      724 725
Sobczyk, A.      724 725 800
Space of type A      766
Space, $B-\omega(\{G_{j}\})$       802
Spectral family      827
Steckin, S.B.      787
Steinhaus, H.      758 760 831
Sternbach, L.      755 762 765
Straus, E.G.      729 756
Strongly series summable M-basis      386
Strongly series summable M-basis, boundedly complete      396
Subramanian, P.K.      803
Subreflexive      662
Subspace factorization property      725
Subspace factorization property for $L^{p}$       725
Subspace of an orthogonally scattered measure      816
Subspace, prebasic      866
Subspace, quasi-basic      866
Subspace, strong      729
Sudakov, V.N.      759
Summation field      828
Sundaresan, K.      866
Symmetric gauge function      803
Symmetric norm      803
Szankowski, A.      721 723 726 817 818 856 861
Szegoe, G.      729
T-basic sequence      374
T-basis (summation basis)      350
T-basis of subspaces      785
T-basis, boundedly complete (as an M-basis)      375
T-basis, shrinking, etc.      375
T-basis, T-boundedly complete      375
T-basis, T-unconditional      376
T-basis, triangular      350
T-basis, weak      375
T-basis, weak*-Schauder      375
T-invariant sequence      190
T-limitable      349
T-summable      349
Taam, C.T.      718 719
Tacon, D.G.      829 830 832
Terenzi, P.      856 857 858 866 867
Thorp, E.      751
Topology of almost uniform convergence      717
Topology of compact convergence      4
Total over a subspace      90
Tr A      711
Transfinite basic sequence (of type $\vartheta$ )      581
Transfinite basic sequence, monotone, etc.      599

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