Examples of weakly compact sets in Orlicz spaces


Орлич кеңiстiктерiндегi әлсiз жинақы жиындардың мысалдары
Примеры слабо компактных множеств в пространствах Орлича
Dauitbek D. Nessipbayev Y. Tulenov K.
2022E.A. Buketov Karaganda University Publish house

Bulletin of the Karaganda University. Mathematics Series
2022#106Issue 272 - 82 pp.

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.

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

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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Al-Farabi Kazakh National University, Almaty, Kazakhstan

Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University

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