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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

1. Ando, T., Linear-functionals on Orlicz spaces, Nieuw Arch. Wisk. (3) 8(1960), 1–16.Google Scholar
2. Grzaslewicz, R., Hudzik, H. and Kurc, W., Extreme and exposed points in Orlicz spaces, Can. J. Math (3) 44(1992).Google Scholar
3. Hudzik, H. and Mastylo, M., Strongly extreme points in Köthe-Bochner spaces, to appear.Google Scholar
4. Krasnoselskii, M. A. and Ya. Rutickii, B., Convex functions and Orlicz spaces, Groningen, 1961, (translation).Google Scholar
5. Kurc, W., Strongly extreme points in Orlicz spaces with the Luxemburg norm, to appear.Google Scholar
6. Luxemburg, W. A. J., Banach function spaces, Thesis, Delft, 1955.Google Scholar
7. Musielak, J., Orlicz spaces and modular spaces, Lecture Notes in Math. 1034, Springer-Verlag, 1983.Google Scholar
8. Smith, M. A., Strongly extreme points in Lp(μ,X), Rocky Mtn. J. Math. 16(1986), 1–5.Google Scholar