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On Čebyšev subspaces and unconditional bases in Banach spaces
Author:
J. R. Retherford
Journal:
Bull. Amer. Math. Soc. 73 (1967), 238-241
MathSciNet review:
0208342
Full-text PDF
References |
Additional Information
- 1.
C.
Bessaga and A.
Pełczyński, On bases and unconditional convergence of
series in Banach spaces, Studia Math. 17 (1958),
151–164. MR 0115069
(22 #5872)
- 2.
M. M. Day, Normed linear spaces, Springer, Berlin, 1962.
- 3.
I.
M. Gel′fand, Remark on the work of N. K. Bari,
“Biorthogonal systems and bases in Hilbert space.”,
Moskov. Gos. Univ. Učenye Zapiski Matematika 148(4)
(1951), 224–225 (Russian). MR 0050172
(14,289c)
- 4.
M.
M. Grinblyum, On the representation of a space of type 𝐵 in
the form of a direct sum of subspaces, Doklady Akad. Nauk SSSR (N.S.)
70 (1950), 749–752 (Russian). MR 0033977
(11,525c)
- 5.
V.
Istrăţescu, Über die Banachräme mit
zählbarer Basis. I, Rev. Math. Pures Appl. (Bucarest)
7 (1962), 481–482 (German). MR 0178332
(31 #2590)
- 6.
C.
W. McArthur and J.
R. Retherford, Some applications of an inequality in
locally convex spaces, Trans. Amer. Math.
Soc. 137 (1969),
115–123. MR 0239391
(39 #748), http://dx.doi.org/10.1090/S0002-9947-1969-0239391-0
- 7.
V.
N. Nikol′skiĭ, Best approximation and basis in
Fréchet space, Doklady Akad. Nauk SSSR (N. S.)
59 (1948), 639–642 (Russian). MR 0026243
(10,128a)
- 8.
V.
N. Nikol′skiĭ, Some questions of best approximation in
a function space, Uč. Zap. Kalininsk. Pedagog. Inst.
16 (1953), 119–160 (1954) (Russian). MR 0071728
(17,175j)
- 9.
R.
R. Phelps, Čebyšev subspaces of finite codimension in
𝐶(𝑋), Pacific J. Math. 13 (1963),
647–655. MR 0156137
(27 #6069)
- 10.
I.
Singer, On a theorem of I. M. Gel′fand, Uspehi Mat. Nauk
17 (1962), no. 1 (103), 169–176 (Russian). MR 0133670
(24 #A3496)
- 11.
I. Singer, Baze in spatii Banach. III, Studii şi Cercetari Maternatice 15 (1964), 675-679.
- 12.
B.
E. Veĭc, Some properties of stability of bases, Dokl.
Akad. Nauk SSSR 158 (1964), 13–16 (Russian). MR 0177281
(31 #1544)
- 1.
- C. Bessaga and A. Pełczynski, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151-164. MR 115069
- 2.
- M. M. Day, Normed linear spaces, Springer, Berlin, 1962.
- 3.
- I. M. Gelfand, Remark on the work of N. K. Bari, "Biorthogonal systems and bases in Hilbert space," Moskov. Gos. Univ. Učen. Zap. 148, Mathematika 4 (1951), 224-225 (Russian). MR 50172
- 4.
- M. M. Grimblyum, On the representation of a space of type B in the form of a direct sum of subspaces, Dokl. Akad. Nauk. SSSR 70 (1950), 749-752 (Russian). MR 33977
- 5.
- V. Istratescu, Über die Banachräume mit Zahlbarer Basis. I, Rev. Math. Pures Appl. 7 (1962), 481-482. MR 178332
- 6.
- C. W. McArthur and J. R. Retherford, Some applications of an inequality in locally convex spaces, Trans. Amer. Math. Soc. (to appear). MR 239391
- 7.
- V. N. Nikol'skiĭ, Best approximation and basis in Fréchet spaces, Dokl. Akad. Nauk. SSSR 59 (1948), 639-692 (Russian). MR 26243
- 8.
- V. N. Nikol'skiĭ, Some questions of best approximation in function spaces, Učen. Zap. Kalininsk. State Ped. Inst. 16 (1953), 119-160 (Russian). MR 71728
- 9.
- R. R. Phelps, Čebyšev subspaces of finite codimension in C(X), Pacific J. Math. 13(1963), 647-655. MR 156137
- 10.
- I. Singer, On a theorem of I. M. Gelfand, Uspehi Mat. Nauk. 17 (1962), no. 1 (103), 169-176 (Russian). MR 133670
- 11.
- I. Singer, Baze in spatii Banach. III, Studii şi Cercetari Maternatice 15 (1964), 675-679.
- 12.
- B. E. Veic, Some stability properties of bases, Dokl. Akad. Nauk SSSR 158 (1964), 13-16 = Soviet Math. Dokl. 5 (1964), 1141-1144. MR 177281
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1967-11698-7
PII:
S 0002-9904(1967)11698-7
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