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Orlicz spaces which are noncreasy

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Abstract.

It is proved that a Banach space X is noncreasy whenever X is rotund or smooth. It is also shown that if a Banach space X is uniformly noncreasy, then any point of its unit sphere is either strongly extreme or Frechét differentiable. Some another general result concerning noncreasy Banach spaces and midpoint locally uniformly rotund Banach spaces is proved. Criteria in order that Orlicz spaces are noncreasy are given.

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Authors and Affiliations

  1. Department of Mathematics, Harbin University of Science and Technology, Xuefu Road 52,¶ 150080 Harbin, P. R. China, e-mail: cuiya@hkd.hrbust.edu.cn, , , , , , CN

    Y. Cui

  2. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49,¶ 60-769 Poznan, Poland, , , , , , PL

    H. Hudzik

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  1. Y. Cui
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  2. H. Hudzik
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Eingegangen am 27. 1. 1999

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Cui, Y., Hudzik, H. Orlicz spaces which are noncreasy. Arch. Math. 78, 303–309 (2002). https://doi.org/10.1007/s00013-002-8251-z

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  • DOI: https://doi.org/10.1007/s00013-002-8251-z

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