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Journal of Convex Analysis 21 (2014), No. 1, 147--166
Copyright Heldermann Verlag 2014

λ-Points in Orlicz Spaces

Adam Bohonos
School of Mathematics, West Pomeranian University of Technology, Al. Piastów 48/49, 70-310 Szczecin, Poland

Ryszard Pluciennik
Institute of Mathematics, Poznan University of Technology, Piotrowo 3A, 60-965 Poznan, Poland

A criterion for λ-points of the unit ball in Orlicz spaces generated by arbitrary Orlicz functions (that is Orlicz functions which vanish outside zero and which attain infinite values to the right of some point u>0 are not excluded) and equipped with the Orlicz norm is given. Moreover, Orlicz spaces with the λ-property are characterized. In contrast to results of H. Y. Sun and C. X. Wu [λ-property of Orlicz space LM, Comment. Math. Univ. Carolin. 31 (1990) 731-741], Orlicz spaces considered by us need not always have the λ-property.

Keywords: Orlicz space, lambda-point, lambda-property, extreme point, Orlicz norm.

MSC: 46E30, 46E40, 46B20

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