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K-extreme point of generalized Orlicz sequence spaces with Luxemburg norm

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Shi Z. , Wang X.

tom Vol. 53, No. 2

147--162

In this paper,we give necessary and sufficient conditions in order that a point u∈S(l(Φ)) is a k-extreme point in generalized Orlicz sequence spaces equipped with the Luxemburg norm, combing the methods used in classical Orlicz spaces and new methods introduced especially for generalized ones. The results indicate the difference between the classical Orlicz spaces and generalized Orlicz spaces.

On the frame of the unit ball of Banach spaces

100%

Tanaka R.

nr 11

1700-1713

The notion of the frame of the unit ball of Banach spaces was introduced to construct a new calculation method for the Dunkl-Williams constant. In this paper, we characterize the frame of the unit ball by using k-extreme points and extreme points of the unit ball of two-dimensional subspaces. Furthermore, we show that the frame of the unit ball is always closed, and is connected if the dimension of the space is not less than three. As infinite dimensional examples, the frame of the unit balls of c 0 and ℓ p are determined.