Weak compactness criteria in $L_1$ space in terms of Orlicz function
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866929256867561472 |
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| author | Nessipbayev, Yerlan Tulenov, Kanat |
| author_facet | Nessipbayev, Yerlan Tulenov, Kanat |
| contents | In this paper, we provide a direct proof for the equivalence of K.M. Chong's and De la Vallée 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 $L_1(0, \infty)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_12578 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Weak compactness criteria in $L_1$ space in terms of Orlicz function Nessipbayev, Yerlan Tulenov, Kanat Operator Algebras Functional Analysis In this paper, we provide a direct proof for the equivalence of K.M. Chong's and De la Vallée 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 $L_1(0, \infty)$. |
| title | Weak compactness criteria in $L_1$ space in terms of Orlicz function |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2004.12578 |