Weak compactness criteria in $L_1$ space in terms of Orlicz function

Yerlan Nessipbayev; Kanat Tulenov

Weak compactness criteria in $L_1$ space in terms of Orlicz function

Operator Algebras 2024-02-28 v5 Functional Analysis

Authors: Yerlan Nessipbayev , Kanat Tulenov

Abstract

In this paper, we provide a direct proof for the equivalence of K.M. Chong's and De la Vall\'{e}e Poussin's criteria of weak compactness of a subset $K$ of $L_1(0,1)$ in terms of some Orlicz function. Furthermore, we discuss the equivalence in $L_1(0, \infty)$ .

Keywords

weak compactness l1 space orlicz function chong criterion de la vallee poussin criterion

Cite

@article{arxiv.2004.12578,
  title  = {Weak compactness criteria in $L_1$ space in terms of Orlicz function},
  author = {Yerlan Nessipbayev and Kanat Tulenov},
  journal= {arXiv preprint arXiv:2004.12578},
  year   = {2024}
}

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