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 Φ is not bounded by the modular Φ, then it is possible for a set K to remain unbounded under any modular Ψ increasing more rapidly than Φ.

Keywords

• conjugate (complementary) functions
• relative weak compactness
• Orlicz spaces, N−functions