Examples of weakly compact sets in Orlicz spaces

Dostilek Dauitbek, Y. Nessipbayev, Kanat Tulenov

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2022

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DOI 10.31489/2022m2/72-82

Data confidence 70 medium

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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 LΦ 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.