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Weakly convergent sequence coefficient
in Köthe sequence spaces

Author: Yunan Cui
Journal: Proc. Amer. Math. Soc. 126 (1998), 195-201
MSC (1991): Primary 46B20, 46B30, 46E20
MathSciNet review: 1343687
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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.

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  • 1. W. L. Bynum, Normal structure coefficients for Banach spaces, Pacific J. Math. 86 (1980), 427-436. MR 81m:46030
  • 2. Guanglu Zhang, Weakly convergent sequence coefficient of product space, Proc. Amer. Math. Soc. 117 (1993), 637-643. MR 93d:46037
  • 3. To[??]mas Do[??]minguez Benavides, Weak uniform normal structure in direction sum spaces, Studia Math. 103 (37) (1992), 283-290. MR 94c:46024
  • 4. M. S. Brodskii and D. P. Milman, On the center of a convex set, Dokl. Akad. Nauk SSSR 59 (1948), 837-840. MR 9:448f
  • 5. S. Chen, Geometric theory of Orlicz spaces, Dissertation Math., 1996.
  • 6. R. Goebel and W. A. Kirk, Topics in metric fixed point theory, Cambridge University Press, 1990. MR 92c:47070
  • 7. F. Hiai, Representation of additive functional on vector-valued normed Köthe spaces, Kodai Math. J. 2 (1979), 300-313. MR 81d:46037
  • 8. T. C. Lin, On the normal structure coefficient and the bounded sequence coefficient, Proc. Amer. Math. Soc., 88 (1983), 262-264. MR 85g:46021
  • 9. J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, Springer-Verlag, Berlin, Heidelberg and New York, 1977. MR 58:17766
  • 10. E. Maluta, Uniformly normal structure and related coefficients, Pacific J. Math., 111 (1984), 357-369. MR 85j:46023
  • 11. J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Math., vol. 1034, Springer-Verlag, 1983. MR 85m:46028
  • 12. M. M. Rao and Z. D. Ren, Theory of Orlicz spaces, Marcel Dekker Inc., New York, Basel and Hong Kong, 1991. MR 92e:46059
  • 13. H. K. Xu, The Maluta problem of sequence constants in Banach spaces, Bull. Sci. China 34 (1989), 725-726. CMP 90:06

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Additional Information

Yunan Cui
Affiliation: Department of Mathematics, Harbin University of Science and Technology, Harbin City, Heilongjiang 150080, People’s Republic of China

Keywords: Weakly convergent sequence coefficient, K\"othe sequence spaces
Additional Notes: The author was supported by the NSF and ECF of China
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society

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