Weak compactness in nice Musielak-Orlicz spaces
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911402519691264 |
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| author | Sanchiz, Mauro |
| author_facet | Sanchiz, Mauro |
| contents | We prove two weak compactness criteria in Musielak-Orlicz spaces for $N$-functions satisfying the $Δ_2$-condition. They extend criteria from Andô for Orlicz spaces to this setting of non-symmetrical Banach function spaces. As consequences, we prove criteria for a sequence in a Musielak-Orlicz space to be weakly convergent, and show that Musielak-Orlicz spaces with the subsequence splitting property are weakly Banach-Saks. The study includes the case of Musielak-Orlicz sequence spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19512 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weak compactness in nice Musielak-Orlicz spaces Sanchiz, Mauro Functional Analysis 46E30 We prove two weak compactness criteria in Musielak-Orlicz spaces for $N$-functions satisfying the $Δ_2$-condition. They extend criteria from Andô for Orlicz spaces to this setting of non-symmetrical Banach function spaces. As consequences, we prove criteria for a sequence in a Musielak-Orlicz space to be weakly convergent, and show that Musielak-Orlicz spaces with the subsequence splitting property are weakly Banach-Saks. The study includes the case of Musielak-Orlicz sequence spaces. |
| title | Weak compactness in nice Musielak-Orlicz spaces |
| topic | Functional Analysis 46E30 |
| url | https://arxiv.org/abs/2601.19512 |