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

Adam Bohonos;  Ryszard 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 Bohonos;  Ryszard 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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