Examples of weakly compact sets in Orlicz spaces

Abstract

This paper provides a number of examples of relatively weakly compact sets in Orlicz spaces. We show some results arising from these examples. Particularly, we provide a criterion which ensures that some Orlicz function is increasing more rapidly than another (in a sense of T. Ando). In addition, we point out that if a bounded subset K of the Orlicz space L is not bounded by the modular , then it is possible for a set K to remain unbounded under any modular increasing more rapidly than .