1. Examples of weakly compact sets in Orlicz spaces
- Author
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D. Dauitbek, Y. Nessipbayev, and K. Tulenov
- Subjects
Analysis ,QA299.6-433 ,Analytic mechanics ,QA801-939 ,Probabilities. Mathematical statistics ,QA273-280 - 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.
- Published
- 2022
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