On bibasic systems and a Retherford’s problem
Pličko, Anatoli ; Terenzi, Paolo
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 76 (1984), p. 28-34 / Harvested from Biblioteca Digitale Italiana di Matematica

Ogni spazio di Banach ha un sistema bibasico (xn,fn) normalizzato; inoltre ogni successione (xn) uniformemente minimale appartiene ad un sistema biortogonale limitato (xn,fn), dove (fn) è M-basica e normante.

Publié le : 1984-07-01
@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] Banach, S. (1932) - Théorie des operations linéaires. Chelsea Publishing Company, New York. | Zbl 0067.08902

[2] Davis, W.J., Dean, O. and Bor-Luh, L. (1973) - Bibasic systems and norming basic sequences. «Trans. Amer. Math. Soc.», 176, 89-102. | MR 313763 | Zbl 0249.46010

[3] Kransoselskii, M.A., Krein, M.G. and Milman, D.P. (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] Milman, V.D. (1970) - Geometric theory of Banach spaces. Part I. «Russian Math. Surveys», 25, 111-170. | MR 280985 | Zbl 0221.46015

[5] Pelczynski, A. (1966) - Some open questions in functional analysis (A lecture given to Lousiana State University). Dittoed Notes.

[6] Singer, I. (1970) —Best approximation in normed linear spaces by elements of linear subspaces. Berlin-Heidelberg-New York: Springer. | MR 270044 | Zbl 0197.38601

[7] Singer, I. (1970) - Bases in Banach spaces I. Berlin-Heidelberg-New York: Springer. | MR 298399 | Zbl 0198.16601

[8] Singer, I. (1981) - Bases in Banach spaces II. Berlin-Heidelberg-New York: Springer. | MR 610799 | Zbl 0467.46020

[9] Terenzi, P. (1979) — A complement to Krein-Milman-Rutman theorem, with applications. «Ist. Lombardo (Rend. Sc.)», A 113, 341-353. | MR 622113 | Zbl 0465.46005

[10] Terenzi, P. (1983) - Extension of uniformly minimal M-basic sequences in Banach spaces. «J. London Math. Society (2)», 27, 500-506. | MR 697142 | Zbl 0488.46011