Weakly convergent sequence coefficient in Köthe sequence spaces

Cui, Yunan

doi:10.1090/S0002-9939-98-03483-2

Weakly convergent sequence coefficient in Köthe sequence spaces
HTML articles powered by AMS MathViewer

by Yunan Cui PDF

Proc. Amer. Math. Soc. 126 (1998), 195-201 Request permission

Abstract:

In this paper, we have discussed the weakly convergent sequence coefficient in Köthe sequence spaces with $(e_n)$ as their boundedly complete basis. Using those results, we can easily calculate the weakly convergent sequence coefficient in Orlicz sequence spaces.

References

W. L. Bynum, Normal structure coefficients for Banach spaces, Pacific J. Math. 86 (1980), no. 2, 427–436. MR 590555, DOI 10.2140/pjm.1980.86.427
Guang Lu Zhang, Weakly convergent sequence coefficient of product space, Proc. Amer. Math. Soc. 117 (1993), no. 3, 637–643. MR 1152993, DOI 10.1090/S0002-9939-1993-1152993-1
Tomás Domínguez Benavides, Weak uniform normal structure in direct sum spaces, Studia Math. 103 (1992), no. 3, 283–290. MR 1202012, DOI 10.4064/sm-103-3-283-290
Garrett Birkhoff and Morgan Ward, A characterization of Boolean algebras, Ann. of Math. (2) 40 (1939), 609–610. MR 9, DOI 10.2307/1968945
S. Chen, Geometric theory of Orlicz spaces, Dissertation Math., 1996.
Kazimierz Goebel and W. A. Kirk, Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics, vol. 28, Cambridge University Press, Cambridge, 1990. MR 1074005, DOI 10.1017/CBO9780511526152
Fumio Hiai, Representation of additive functionals on vector-valued normed Köthe spaces, Kodai Math. J. 2 (1979), no. 3, 300–313. MR 553237
Teck-Cheong Lim, On the normal structure coefficient and the bounded sequence coefficient, Proc. Amer. Math. Soc. 88 (1983), no. 2, 262–264. MR 695255, DOI 10.1090/S0002-9939-1983-0695255-2
Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 92, Springer-Verlag, Berlin-New York, 1977. Sequence spaces. MR 0500056, DOI 10.1007/978-3-642-66557-8
E. Maluta, Uniformly normal structure and related coefficients, Pacific J. Math. 111 (1984), no. 2, 357–369. MR 734861, DOI 10.2140/pjm.1984.111.357
Julian Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, vol. 1034, Springer-Verlag, Berlin, 1983. MR 724434, DOI 10.1007/BFb0072210
M. M. Rao and Z. D. Ren, Theory of Orlicz spaces, Monographs and Textbooks in Pure and Applied Mathematics, vol. 146, Marcel Dekker, Inc., New York, 1991. MR 1113700
H. K. Xu, The Maluta problem of sequence constants in Banach spaces, Bull. Sci. China 34 (1989), 725–726.