JournalszaaVol. 17, No. 4pp. 893–905

On Some Uniform Convexities and Smoothness in Certain Sequence Spaces

  • Yunan Cui

    University of Science and Technology, Harbin, China
  • Henryk Hudzik

    Adam Mickiewicz University, Poznan, Poland
  • Ryszard Pluciennik

    Adam Mickiewicz University, Poznan, Poland
On Some Uniform Convexities and Smoothness in Certain Sequence Spaces cover
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Abstract

It is proved that any Banach space XX with property A2eA^e_2 has property A2A_2 and that a Banach space XX is nearly uniformly smooth if and only if it is nearly uniformly *- smooth and weakly sequentially complete. It is shown that if XX is a Köthe sequence space the dual of which contains no isomorphic copy of l1l_1 and has property A2eA^e_2, then XX has the uniform Kadec-Klee property. Criteria for nearly uniformly convexity of Musielak-Orlicz spaces equipped with the Orlicz norm are presented. It is also proved that both properties nearly uniformly smoothness and nearly uniformly convexity for Musielak-Orlicz spaces equipped with the Luxemburg norm coincide with reflexivity. Finally, an interpretation of those results for Nakano spaces l(pi)(1<pi<)l^{(p_i)} (1 < p_i < \infty) is given.

Cite this article

Yunan Cui, Henryk Hudzik, Ryszard Pluciennik, On Some Uniform Convexities and Smoothness in Certain Sequence Spaces. Z. Anal. Anwend. 17 (1998), no. 4, pp. 893–905

DOI 10.4171/ZAA/857