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Kadec-Klee property in Musielak-Orlicz function spaces equipped with the Orlicz norm

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Abstract

It is well-known that the Kadec-Klee property is an important property in the geometry of Banach spaces. It is closely connected with the approximation compactness and fixed point property of non-expansive mappings. In this paper, a criterion for Musielak-Orlicz function spaces equipped with the Orlicz norm to have the Kadec-Klee property are given. As a corollary, we obtain that a class of non-reflexive Musielak-Orlicz function spaces have the Fixed Point property.

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Acknowledgements

This work was supported by the Natural Science Foundation of China(11871181).

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Authors and Affiliations

  1. Department of Mathematics, Harbin University of Science and Technology, Harbin, 150080, China

    Yunan Cui & Li Zhao

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  1. Yunan Cui
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  2. Li Zhao
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Correspondence to Yunan Cui.

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To my supervisor, Henryk Hudzik.

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Cui, Y., Zhao, L. Kadec-Klee property in Musielak-Orlicz function spaces equipped with the Orlicz norm. Aequat. Math. 96, 167–184 (2022). https://doi.org/10.1007/s00010-021-00808-8

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