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Weakly Compact Sets and Riesz Representation Theorem in Musielak Sequence Spaces

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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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Authors and Affiliations

  1. Department of Mathematics, Anhui Normal University, Wuhu, 241000, P. R. China

    Wan Zhong Gong

  2. Smeal College of Business, Pennsylvania State University, University Park, Pennsylvania, 16802, USA

    Si Yu Shi

  3. Department of Mathematics, Shanghai University, Shanghai, 200444, P. R. China

    Zhong Rui Shi

Authors
  1. Wan Zhong Gong
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  2. Si Yu Shi
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  3. Zhong Rui Shi
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Correspondence to Zhong Rui Shi.

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Conflict of Interest The authors declare no conflict of interest.

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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

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