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Unconditional bases and best approximation in Banach spaces
Authors:
J. R. Retherford and R. C. James
Journal:
Bull. Amer. Math. Soc. 75 (1969), 108-112
MathSciNet review:
0276735
Full-text PDF
References |
Additional Information
- 1.
Mahlon
M. Day, Strict convexity and smoothness of
normed spaces, Trans. Amer. Math. Soc. 78 (1955), 516–528.
MR
0067351 (16,716a), http://dx.doi.org/10.1090/S0002-9947-1955-0067351-1
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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)
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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)
- 4.
J.
R. Retherford, On Čebyšev subspaces and
unconditional bases in Banach spaces, Bull.
Amer. Math. Soc. 73
(1967), 238–241. MR 0208342
(34 #8152), http://dx.doi.org/10.1090/S0002-9904-1967-11698-7
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R. Retherford, Schauder bases and best approximation, Colloq.
Math. 22 (1970), 91–110. (errata insert). MR 0273374
(42 #8253)
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Singer, On a theorem of I. M. Gel′fand, Uspehi Mat. Nauk
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(24 #A3496)
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Ivan
Singer, Bases in Banach spaces. II, III, Stud. Cerc. Mat. 15
(1964), 157–208; ibid. 16 (1964), 675–725
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0190710 (32 #8121b)
- 1.
- M. M. Day, Strict convexity and smoothness of normed spaces, Trans Amer. Math. Soc. 78 (1955), 516-528. MR 67351
- 2.
- V. N. Nikol'skii, Best approximation and basis in Fréchet spaces, Dokl. Akad. Nauk SSSR 59 (1948), 639-692. (Russian) MR 26243
- 3.
- V. N. Nikol'skii, Some questions of best approximation in a function space, Učen, Zap. Kalininsk. Ped. Inst. 16 (1953), 119-160. (Russian) MR 71728
- 4.
- J. R. Retherford, On Čebyšev subspaces and unconditional bases in Banach space, Bull. Amer. Math. Soc. 73 (1967), 238-241. MR 208342
- 5.
- J. R. Retherford, Schauder bases and best approximation, Collect. Math (to appear). MR 273374
- 6.
- I. Singer, On a theorem of I M. Gel'fand, Uspehi Mat. Nauk 17 (1962), no. 1 (103), 169-176. (Russian) MR 133670
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- I. Singer, Baze in spatii Banach III, Stud Cerc. Mat. 15 (1964), 675-679. MR 190710
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1969-12163-4
PII:
S 0002-9904(1969)12163-4
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