Bounded completeness and Schauder's basis for C[0, 1]
Glasgow mathematical journal, Tome 28 (1986) no. 1, pp. 15-19
Voir la notice de l'article provenant de la source Cambridge University Press
A basis , for a Banach space X is said to be boundedly complete [4, p. 284] if whenever is a sequence of scalars for which converges. It is well-known [2, p. 70] that if is a boundedly complete basis for X then X is isometric to a conjugate space; in fact, X = [fi]*, where is the sequence of coefficient functionals associated with the basis It follows that no basis for C[0,1] can be boundedly complete since no separable conjugate space contains C0[l], yet C[0,1] is a separable space which contains c0.
Holub, J. R. Bounded completeness and Schauder's basis for C[0, 1]. Glasgow mathematical journal, Tome 28 (1986) no. 1, pp. 15-19. doi: 10.1017/S0017089500006273
@article{10_1017_S0017089500006273,
author = {Holub, J. R.},
title = {Bounded completeness and {Schauder's} basis for {C[0,} 1]},
journal = {Glasgow mathematical journal},
pages = {15--19},
year = {1986},
volume = {28},
number = {1},
doi = {10.1017/S0017089500006273},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500006273/}
}
[1] 1.Bessaga, C. and Pelczynski, A., On bases and unconditional convergence of series in Banach spaces, Studio Math. 17 (1958), 151–164. Google Scholar | DOI
[2] 2.Day, M. M., Normed linear spaces (Springer-Verlag, 1962). Google Scholar | DOI
[3] 3.Gohberg, I. and Krein, M., Introduction to the theory of linear nonselfadjoint operators, Translations of Mathematical Monographs, Volume 18 (American Mathematical Society, 1969). Google Scholar
[4] 4.Singer, I., Bases in Banach spaces I (Springer-Verlag, 1970). Google Scholar | DOI
Cité par Sources :