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Orlicz Spaces Without Strongly Extreme Points and Without H-Points

Published online by Cambridge University Press:  20 November 2018

Henryk Hudzik
Henryk Hudzik*
Affiliation:
Institute of Mathematics Adam Mickiewicz University Matejki 48/49 60-769 Poznan Poland
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Abstract

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W. Kurc [5] has proved that in the unit sphere of Orlicz space LΦ(μ) generated by an Orlicz function Φ satisfying the suitable Δ2-condition and equipped with the Luxemburg norm every extreme point is strongly extreme. In this paper it is proved in the case of a nonatomic measure μ that the unit sphere of the Orlicz space LΦ(μ) generated by an Orlicz function Φ which does not satisfy the suitable Δ2-condition and equipped with the Luxemburg norm has no strongly extreme point and no H-point.

Keywords

46E3046B20Orlicz spaceLuxemburg normΔ2-conditionstrongly extreme pointH-point.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 2 , 01 June 1993 , pp. 173 - 177
Copyright
Copyright © Canadian Mathematical Society 1993

References

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