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Metric projections and best approximants in Bochner-Orlicz spaces.

Ryszard PluciennikYuwen Wang — 1994

Revista Matemática de la Universidad Complutense de Madrid

In the first section of this paper there are given criteria for strict convexity and smoothness of the Bochner-Orlicz space with the Orlicz norm as well as the Luxemburg norm. In the second one that geometrical properties are applied to the characterization of metric projections and zero mean valued best approximants to Bochner-Orlicz spaces.

A strongly extreme point need not be a denting point in Orlicz spaces equipped with the Orlicz norm

Adam BohonosRyszard Płuciennik — 2011

Banach Center Publications

There are necessary conditions for a point x from the unit sphere to be a denting point of the unit ball of Orlicz spaces equipped with the Orlicz norm generated by arbitrary Orlicz functions. In contrast to results in [12, 17, 16], we present also examples of Orlicz spaces in which strongly extreme points of the unit ball are not denting points.

Modulus of dentability in L ¹ + L

Adam BohonosRyszard Płuciennik — 2008

Banach Center Publications

We introduce the notion of the modulus of dentability defined for any point of the unit sphere S(X) of a Banach space X. We calculate effectively this modulus for denting points of the unit ball of the classical interpolation space L ¹ + L . Moreover, a criterion for denting points of the unit ball in this space is given. We also show that none of denting points of the unit ball of L ¹ + L is a LUR-point. Consequently, the set of LUR-points of the unit ball of L ¹ + L is empty.

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