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Orlicz sequence spaces that are uniformly rotund in a weakly compact set of directions. (English) Zbl 1117.46013

Summary: Necessary and sufficient conditions are given for Orlicz sequence spaces equipped with the Orlicz norm to be uniformly rotund in a weakly compact set of directions, using only conditions on the generating function of the space.

MSC:

46B20 Geometry and structure of normed linear spaces
46B45 Banach sequence spaces