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Weakly compact sets in Orlicz sequence spaces

Siyu Shi; Zhong Rui Shi; Shujun Wu — 2021

Czechoslovak Mathematical Journal

We combine the techniques of sequence spaces and general Orlicz functions that are broader than the classical cases of $N$ -functions. We give three criteria for the weakly compact sets in general Orlicz sequence spaces. One criterion is related to elements of dual spaces. Under the restriction of ${lim}_{u \to 0} M (u) / u = 0$ , we propose two other modular types that are convenient to use because they get rid of elements of dual spaces. Subsequently, by one of these two modular criteria, we see that a set $A$ in Riesz spaces $l_{p}$ ...

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