Abstract

It is proved that for any reflexive Banach space X, both X and X∗X^* are CLUR if and only if both X and X∗X^* have property H. Criteria for rotundity, local uniform rotundity, compact local uniform rotundity and property H in Orlicz sequence spaces equipped with the Orlicz norm are given. Criteria for property H, rotundity and LUR were already known in the literature only for finitely valued Orlicz functions which vanish only at zero and are N-functions (i.e. they satisfy conditions (0₁) and (∞₁). All our criteria except Corollary 2.15 are given for arbitrary Orlicz functions. Criteria for smoothness of lΦ0l^0_\Phi in Corollary 2.15 are given for any finitely valued Orlicz function satisfying condition (∞₁), extending the respective result of Chen, Hudzik and Wisla proved only for Orlicz functions vanishing only at zero.

Author information

Contact details are reproduced from the original publication and may be historical.

Yunan Cui

Dept. of Mathematics, Harbin University of Science and Technology, Xuefu Road 52, 150080 Harbin, P. R. China

Henryk Hudzik

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, U. Matejki 48/49, 60-769 Poznań, Poland

Marian Nowak

Inst. of Mathematics, T. Kotarbiński Pedagogical University, Pl. Słowiański 9, 65-069 Zielona Góra, Poland

Ryszard Płuciennik

Inst. of Mathematics, University of Technology, Piotrowo 3A, 60-965 Poznań, Poland

Keywords

  • Orlicz sequence space
  • compact local uniform rotundity
  • property H
  • smoothness
  • copy of l-sub-infinity

Mathematics Subject Classification

46E30; 46E40, 46B20

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Suggested citation

Y. Cui, H. Hudzik, M. Nowak, R. Płuciennik. “Some Geometric Properties in Orlicz Sequence Spaces Equipped with Orlicz Norm.” Journal of Convex Analysis 6 (1999), No. 1, 91–113. https://doi.org/10.68381/jca06007

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Published by Heldermann Verlag, 1999. Rights now held by Banach Press LLC.