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Singer I. — Bases in Banach spaces II
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: en

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
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Предметный указатель
$(B_{1} \times B_{2} \times ...)_{l^{1}}$      241
$(C, \alpha)$      358
$(C,\ \alpha)$-basis      358
$(E, \{x_{n}\})^{d}$      263
$(E^{*})^{\#}$      550
$(G_{1} \times G^{2} \times ...)_{l^{p}}$      425
$(G_{1} \times G_{2} \times ...)_{c_{0}}$      425
$(I,\ \mathscr{D})$-conditional basis      811
$(I,\ \mathscr{D})$-conditional decomposition ($(I,\ \mathscr{D})$-conditional basis of subspaces)      826
$(I,\ \mathscr{D})$-conditional Schauder decomposition      826
$(K_{1})$      204
$(K_{2})$      330
$(X, T, \mathfrak{M})$      601
$(X, T, \{Q_{n}\}, \mathfrak{M})$      551
$(\ )^{\bot}$      61
$(\ )_{\bot}$      48
$(\widehat{G; Y})$      48
$2^{[1, n]}$      10
$A_{0}(\{x_{n}\})$      38
$A_{1}$      152 553
$A_{1}^{(T)}$      351
$A_{1}^{(u)}$      153
$A_{1}^{(v)}$      341
$A_{1}^{(\vartheta)}$      583
$ba(\mathcal{N})$      196
$bv^{2}$      366
$B_{1}$      768
$B_{2}$      768
$B_{\nu}$      820
$B_{\nu}$-space      820
$c_{0}$-decomposition      531
$c_{0}(\Gamma)$      6 579
$c_{0}^{(\vartheta)}$      591
$C_{E}$      349
$C_{E}([1, \omega])$      581
$C_{p}$      425
$D_{0}$      504
$d_{1}$      487
$D_{1}^{(u)}$      541
$D_{1}^{(w)} = D_{1}^{(w)}(\{G_{n}\})$      519
$D_{1}^{(\vartheta)}$      623
$D_{2}$      500
$D_{3}$      513
$D_{4}$      512
$d_{5}$      513
$d_{6}$      513
$D_{8}$      525
$D_{E^{*}}(G)$      662
$E^{(n)}$      508
$E^{h}$      660
$E_{(r)}$      35
$E_{0}$      415 542 811
$E_{b}$      294
$Fr S_{E}$      38
$f_{j}^{n}$      29
$f_{w}$      15
$f_{x}$      659
$G^{\bot}$      61
$G_{n, k}$      13
$G_{N}$      26
$H_{n}$      26
$H_{X}$      659
$I_{E}$      1
$l^{1}$-system      864
$l^{1}(m)$-system      864
$l^{p}$-decomposition      531
$l^{p}(\Gamma)$      6 579
$l_{R}^{p}$      36
$l_{\mathfrak{m}}^{\infty}(I)$      861
$M(E, (G_{n}, v_{n}))$      500
$M(E, (x_{n}, f_{n}))$      190
$M(u, (S_{1}, S_{2}))$      802
$M(x, (G_{n}, v_{n}))$      500
$M(z, (x_{n}, f_{n}))$      191
$P_{(n)}$      49
$P_{n}(\{\alpha_{j}\})$      190
$r_{G}(V)$      90
$r_{j}(g)$      9
$r_{V}(G)$      90
$S(E, \{f_{n}\})$      189
$s(\{G_{d}\}_{d\in\mathscr{D}})$      824
$s(\{G_{n}\})$      514
$supp\ x_{i}$      6
$S^{\beta}(\{G_{n}^{*}\})$      514
$S^{\gamma}(\{G_{n}^{*}\})$      514
$S_{E}$      38
$S_{\beta}(\{G_{n}\})$      514
$S_{\gamma}(\{G_{n}\})$      515
$S_{\lambda}(x)$      586
$s_{\{i_{k}\}, n}(x)$      575
$s_{\{\beta_{n}\}, d}(x)$      579
$T_{1}$      823
$T_{2}$      824
$T_{nm}$      370
$u_{E}$      511
$v(I_{0})$      576
$V_{a}$      200
$v_{\{e_{n}\}}^{(s)}$      803
$v_{\{x_{n}\}}$      49 284
$v_{\{x_{n}\}}^{(u)}$      309
$v_{\{\gamma_{n}\}}$      199
$W^{+}$      9
$W^{-}$      9
$w_{ij}^{n}$      763
$w_{j}$      26
$W_{n, k}^{+}$      13
$W_{n, k}^{-}$      13
$W_{n}^{+}$      26
$W_{n}^{-}$      26
$x_{j}^{n}$      28
$x_{w}$      13
$x_{\{\gamma_{n}\}}$      198
$\alpha_{u}$      109
$\alpha_{\{x_{n}\}}$      103
$\approx$      210 507
$\beta$-dual      514
$\beta$-perfect      515
$\beta$-predual (sub-$\beta$ dual)      515 802
$\beta(G)$      768
$\beta\mathscr{N}$      592
$\beta_{n}$      768
$\beta_{u}$      109
$\beta_{\{x_{n}\}}$      106
$\bot$      729
$\chi(A, B)$      793
$\chi_{A}$      208
$\chi_{n}$      515
$\cong$      36
$\Delta(A, B)$      793
$\delta(E)$      795
$\Delta\gamma_{n}$      365
$\Delta^{2}\gamma_{n}$      365
$\equiv$      55
$\eta$-equivalent      50 168
$\gamma$-basis      404
$\gamma$-dual      514
$\gamma$-perfect      515
$\gamma$-predual (sub-$\gamma$ dual)      515 802
$\gamma(E)$      308
$\Gamma(n)$      768
$\Gamma^{(u)}(E)$      866
$\gamma_{\{x_{n}\}}$      49
$\gamma_{\{x_{n}\}}^{(u)}$      866
$\gg$      132 507
$\lambda$      141
$\lambda$-approximation property ($\lambda$-metric)      291 768
$\lambda$-approximative basis      275
$\Lambda(E)$      770
$\Lambda_{\sigma}$      381
$\mathfrak{A}$      514
$\mathfrak{M}$      141
$\mathfrak{M}$-space      824
$\mathfrak{M}BK$-space      824
$\mathfrak{M}_{\{i_{n}\}}$      148
$\mathscr{B}_{\mu}$      816
$\mathscr{C}(E, E)$      518
$\mathscr{C}_{\{x_{n}\}}$      564
$\mathscr{E}$      23
$\mathscr{E}_{0}^{(T)}$      361
$\mathscr{E}_{1}$      91
$\mathscr{E}_{1}^{(T)}$      361
$\mathscr{E}_{2}$      91
$\mathscr{E}_{2}^{(T)}$      361
$\mathscr{E}_{3}^{(T)}$      361
$\mathscr{E}_{c}$      799
$\mathscr{F}$      422
$\mathscr{F}_{n}$      423
$\mathscr{K}_{(x_{n}, f_{n})}$      564
$\mathscr{K}_{\{e_{n}\}}$      560
$\mathscr{L}_{P}$-space      536 821
$\mathscr{M}(S_{1}, S_{2})$      518
$\mathscr{N}$      55
$\mathscr{P}$      587
$\mathscr{P}_{x}$      566
$\mathscr{P}_{\lambda}$      497
$\mathscr{P}_{\lambda}$-space      497 800
$\mathscr{S}(E,\ (x_{n}, f_{n}))$      259
$\mathscr{S}_{n}$      64
$\mathscr{S}_{x}$      574
$\mathscr{T}(M, u)$      5
$\mu_{n}(y)$      140 380
$\omega$      581
$\omega$-linearly independent sequence      104
$\omega$-linearly independent sequence of subspaces      501 801
$\omega_{0}$      822
$\omega_{T}$-linearly independent sequence      786
$\omega_{\alpha}$      648
$\overline{co} M$      40
$\Phi_{+}$-operator      109
$\Phi_{T} = \Phi_{\{e_{n}\}, T}$      786
$\pi = \pi_{E}$      38 511
$\Pi$-basis      409
$\pi$-basis (Schauder operator basis, $\pi$ system)      407 791
$\pi$-basis, strict      407
$\pi$-basis, weak      409
$\pi$-basis, weak*      409
$\pi$-ring      801
$\pi$-space      791
$\pi(E)$      792
$\pi^{\infty}_{1}$-basis ($\pi^{\infty}_{1}$ decomposition)      417 792
$\pi^{\infty}_{1}$-space      792
$\Pi_{1}$      92
$\pi_{G}(x)$      334
$\Pi_{\lambda}$-basis      407
$\pi_{\lambda}$-basis ($\pi_{\lambda}$ decomposition, $\pi_{\lambda}$ system)      407 791
$\pi_{\lambda}$-basis, strict      407
$\pi_{\lambda}$-basis, weak      409
$\pi_{\lambda}$-basis, weak*      409
$\pi_{\lambda}$-space      791
$\pi_{\lambda}$-space, dual      793
$\rho$      475 663
$\rho(A, B)$      793
$\Sigma^{*}$      98
$\sigma_{G}$      49
$\sigma_{j}^{n}$      28
$\sigma_{nm}(x)$      350
$\sigma_{n}$      370
$\sigma_{n}(x)$      350
$\sim$      47 67 203 498
$\succ$      115
$\tau_{j}^{n}$      28
$\tau_{n}(x)$      386 404
$\theta(G, F)$      533
$\theta_{\mathscr{M}}(t)$      560
$\theta_{\{x_{n}\}}(t)$      564
$\tilde{a}$      64
$\tilde{v}(f)$      659
$\underrightarrow{V}$      54
$\underset{\approx}{\sim}$      209 507
$\varepsilon$-close      411
$\varepsilon$-isometry      120
$\varkappa_{u}$      109
$\varkappa_{\{x_{n}\}}$      106
$\vartheta$-linearly independent transfinite sequence      814
$\vartheta$-linearly independent transfinite sequence of subspaces      830
$\{\lambda_{i}\}$-linearly independent sequence      155
$\|f\|_{d}$      822
$\|f\|_{n}$      81 524
$\|u\|_{N}$      258
$\|x\|_{V}$      92
$\|\{\gamma_{n}\}\|_{bv^{2}}$      366
$\|\{\gamma_{n}\}\|_{bv}$      365
$\||x\||_{(T)}$      361
($[h_{n}]$, $\{h_{n}\}$)-near      115
($[h_{n}]$, $\{h_{n}\}$)-near, weakly      115
($\alpha$, $\lambda$)-approximation property      304
(F)      704
(F)-norm      704
(F)-space      704
(p, r)      381
a(E)      518
A(E, E)      518
A.f.c.f. = associated family of coefficient functionals      574
A.f.f. = associated family of functionals      691
A.s.c.f. = associated sequence of coefficient functionals      47
A.s.c.p. = associated sequence of coordinate projections      486
A.s.f. = associated sequence of functionals      166
A.t.s.c.f. = associated transfinite sequence of coefficient functionals      582
A.t.s.c.p. = associated transfinite sequence of coordinate projections      622
Acute angled sequence      564
Acute angled set      560
AD-space      190
Admissible mapping      189
Admissible sequence for a generalized basis      189
Admissible sequence for a quasi-basis      278
Admissible sequence for a quasi-decomposition      539
Admissible space      717
AK-space      190
Alexander, F.E.      864
Altshuler, Z.      751 864
Amir, D.      828 829 832 833
Angular modulus of a sequence      564
Angular modulus of a set      560
Approximation problem      717
Approximation property      5
Approximation property, $\lambda$-duality      314
Approximation property, $\lambda$-projection      413
Approximation property, $\lambda$-uniform      818
Approximation property, $\lambda$-uniform projection      818
Approximation property, bounded      291
Approximation property, bounded compact      724
Approximation property, bounded projection      413
Approximation property, compact      724
Approximation property, metric      291
Approximation property, projection      413
Approximation property, separable range      817
Approximation property, uniform      818
Approximation property, uniform projection      818
Approximative basis      275
Approximative basis of elements      275
Approximative basis of operators      275
Approximative basis, $\lambda$-projection      413
Approximative basis, projection      413
Approximative basis, weak      323
Approximative basis, weak*      323
Aronszajn, N.      766
Arsove, M.G.      758 759 810 811 832
Ascending function      649
Ascending function, strictly      587 649
Asplund, E.      834
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