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arXiv · 2601.19512

Weak compactness in nice Musielak-Orlicz spaces

Mauro Sanchiz
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Abstract

We prove two weak compactness criteria in Musielak-Orlicz spaces for $N$-functions satisfying the $\Delta_2$-condition. They extend criteria from And\^o 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.

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Mauro Sanchiz. 2026-01-27. Weak compactness in nice Musielak-Orlicz spaces. https://arxiv.org/abs/2601.19512

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