Abstract
In this work, we give some criteria of the weakly compact sets and a representation theorem of Riesz’s type in Musielak sequence spaces using the ideas and techniques of sequence spaces and Musielak function. Finally, as an immediate consequence of the criteria considered in this paper, the criteria of the weakly compact sets of Orlicz sequence spaces are deduced.
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In memory of Professor Henryk Hudzik, a great man, our teacher and colleague
Supported by the National Natural Science Foundation of China (Grant No. 11771273)
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Gong, W.Z., Shi, S.Y. & Shi, Z.R. Weakly Compact Sets and Riesz Representation Theorem in Musielak Sequence Spaces. Acta. Math. Sin.-English Ser. 40, 467–484 (2024). https://doi.org/10.1007/s10114-023-1076-3
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DOI: https://doi.org/10.1007/s10114-023-1076-3