Applications of spreading models to regular methods of summabilities and growth rate of Cesàro means

Nolio OKADA; Takashi ITO

doi:10.2969/jmsj/04440591

Nolio OKADA, Takashi ITO

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JOURNAL FREE ACCESS

1992 Volume 44 Issue 4 Pages 591-612

DOI https://doi.org/10.2969/jmsj/04440591

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Published: 1992 Received: September 04, 1991 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. Baernstein, On reflexivity and summability, Studia Math., 42 (1972), 91-94.
2) S. Banach and S. Saks, Sur la convergence forte dans les champs L^p, Studia Math., 2 (1930), 51-57.
3) B. Beauzamy, Banach-Saks properties and spreading models, Math. Scand., 44 (1979), 357-384.
4) B. Beauzamy and J. T. Lapresté, Modèles étalés des espace de Banach, Editéurs des science et des arts, Hermann, Paris, 1984.
5) C. Bessaga and A. Pelczinski, On basis and unconditional convergence of series in Banach spaces, Studia Math., 17 (1958), 151-164.
6) A. Brunel and L. Sucheston, On B-convex Banach spaces, Math. Systems Theory, 7 (1974), 294-299.
7) C. L. DeVito, Functional Analysis, Pure Appl. Math., 81, Academic Press, New York, 1978.
8) L. E. Dor, On sequences spanning a complex l₁ space, Proc. Amer. Math. Soc., 47 (1975), 515-516.
9) P. Erdös and M. Magidor, A note on regular methods of summability and the Banach-Saks property, Proc. Amer. Math. Soc., 59 (1976), 232-234.
10) J. Hoffmann-Jorgensen, Sums of independent Banach space valued random variables, Studia Math., 52 (1974), 159-186.
11) J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Function Spaces, Ergebnisse der Mathematik und ihrer Grenzgebite, 97, Springer, Berlin-Heidelberg- New York, 1979.
12) B. Maurey and G. Pisier, Séries de variables aléatoires vectorielles indépendantes et propriété géométriques des espace de Banach, Studia Math., 58 (1976), 45-90.
13) S. Mazur, Uber konvexe Mengen in linearen normierten Räumen, Studia Math., 4 (1933), 70-84.
14) J. R. Partington, On the Banach-Saks property, Math. Proc. Cambridge Philos. Soc., 82 (1977), 369-374.
15) H. P. Rosenthal, A characterization of Banach spaces containing l₁, Proc. Nat. Acad. Sci. USA, 71 (1974), 2411-2413.
16) H. P. Rosenthal, Weakly independent sequences and the Banach-Saks property, Bull. London Math. Soc., 8 (1976), 22-24.
17) I. Singer, A remark on reflexivity and summability, Studia Math., 26 (1965), 113-114.
18) I. Singer, Bases in Banach Spaces I, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, 154, Springer, Berlin-Heidelberg-New York, 1970.

Right : [1] A. Baernstein, On reflexivity and summability, Studia Math., 42 (1972), 91-94.
[2] S. Banach and S. Saks, Sur la convergence forte dans les champs L^p, Studia Math., 2 (1930), 51-57.
[3] B. Beauzamy, Banach-Saks properties and spreading models, Math. Scand., 44 (1979), 357-384.
[4] B. Beauzamy and J. T. Lapresté, Modèles étalés des espace de Banach, Editéurs des science et des arts, Hermann, Paris, 1984.
[5] C. Bessaga and A. Pelczinski, On basis and unconditional convergence of series in Banach spaces, Studia Math., 17 (1958), 151-164.
[6] A. Brunel and L. Sucheston, On B-convex Banach spaces, Math. Systems Theory, 7 (1974), 294-299.
[7] C. L. DeVito, Functional Analysis, Pure Appl. Math., 81, Academic Press, New York, 1978.
[8] L. E. Dor, On sequences spanning a complex l₁ space, Proc. Amer. Math. Soc., 47 (1975), 515-516.
[9] P. Erdös and M. Magidor, A note on regular methods of summability and the Banach-Saks property, Proc. Amer. Math. Soc., 59 (1976), 232-234.
[10] J. Hoffmann-Jørgensen, Sums of independent Banach space valued random variables, Studia Math., 52 (1974), 159-186.
[11] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Function Spaces, Ergebnisse der Mathematik und ihrer Grenzgebite, 97, Springer, Berlin-Heidelberg-New York, 1979.
[12] B. Maurey and G. Pisier, Séries de variables aléatoires vectorielles indépendantes et propriété géométriques des espace de Banach, Studia Math., 58 (1976), 45-90.
[13] S. Mazur, Uber konvexe Mengen in linearen normierten Räumen, Studia Math., 4 (1933), 70-84.
[14] J. R. Partington, On the Banach-Saks property, Math. Proc. Cambridge Philos. Soc., 82 (1977), 369-374.
[15] H. P. Rosenthal, A characterization of Banach spaces containing l₁, Proc. Nat. Acad. Sci. USA, 71 (1974), 2411-2413.
[16] H. P. Rosenthal, Weakly independent sequences and the Banach-Saks property, Bull. London Math. Soc., 8 (1976), 22-24.
[17] I. Singer, A remark on reflexivity and summability, Studia Math., 26 (1965), 113-114.
[18] I. Singer, Bases in Banach Spaces I, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, 154, Springer, Berlin-Heidelberg-New York, 1970.

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