Ogni spazio di Banach ha un sistema bibasico normalizzato; inoltre ogni successione uniformemente minimale appartiene ad un sistema biortogonale limitato , dove è M-basica e normante.
@article{RLINA_1984_8_77_1-2_28_0,
author = {Anatoli Pli\v cko and Paolo Terenzi},
title = {On bibasic systems and a Retherford's problem},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
volume = {76},
year = {1984},
pages = {28-34},
zbl = {0609.46008},
mrnumber = {0884374},
language = {en},
url = {http://dml.mathdoc.fr/item/RLINA_1984_8_77_1-2_28_0}
}
Pličko, Anatoli; Terenzi, Paolo. On bibasic systems and a Retherford’s problem. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 76 (1984) pp. 28-34. http://gdmltest.u-ga.fr/item/RLINA_1984_8_77_1-2_28_0/
[1] (1932) - Théorie des operations linéaires. Chelsea Publishing Company, New York. | Zbl 0067.08902
[2] , and (1973) - Bibasic systems and norming basic sequences. «Trans. Amer. Math. Soc.», 176, 89-102. | MR 313763 | Zbl 0249.46010
[3] , and (1948) - On defect numbers of linear operators in a Banach space and on some geometric problems. «Sbornik Trud. Inst. Matem. Akad. Nauk Ukr. SSR», 11, 97-112.
[4] (1970) - Geometric theory of Banach spaces. Part I. «Russian Math. Surveys», 25, 111-170. | MR 280985 | Zbl 0221.46015
[5] (1966) - Some open questions in functional analysis (A lecture given to Lousiana State University). Dittoed Notes.
[6] (1970) —Best approximation in normed linear spaces by elements of linear subspaces. Berlin-Heidelberg-New York: Springer. | MR 270044 | Zbl 0197.38601
[7] (1970) - Bases in Banach spaces I. Berlin-Heidelberg-New York: Springer. | MR 298399 | Zbl 0198.16601
[8] (1981) - Bases in Banach spaces II. Berlin-Heidelberg-New York: Springer. | MR 610799 | Zbl 0467.46020
[9] (1979) — A complement to Krein-Milman-Rutman theorem, with applications. «Ist. Lombardo (Rend. Sc.)», A 113, 341-353. | MR 622113 | Zbl 0465.46005
[10] (1983) - Extension of uniformly minimal M-basic sequences in Banach spaces. «J. London Math. Society (2)», 27, 500-506. | MR 697142 | Zbl 0488.46011