Orlicz spaces which are noncreasy

摘要

It is proved that a Banach space X is noncreasy whenever X is rotund or smooth. It is also shown that if a Banach space X is uniformly noncreasy, then any point of its unit sphere is either strongly extreme or Frechét differentiable. Some another general result concerning noncreasy Banach spaces and midpoint locally uniformly rotund Banach spaces is proved. Criteria in order that Orlicz spaces are noncreasy are given.