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Kadec–Klee property with respect to the local convergence in measure of Orlicz–Lorentz spaces

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  • Paweł Foralewski
  • Joanna Kończak

Abstract

In this paper, we find criteria for the Kadec–Klee property with respect to the local convergence in measure in both Orlicz–Lorentz spaces as well as their subspaces of order continuous elements. In the case of Orlicz norm, the presented results are new, whereas in the case of Luxemburg norm, we rely heavily on known results, which we show for the first time as a whole. Finally, we apply the obtained results to Orlicz spaces.

Suggested Citation

  • Paweł Foralewski & Joanna Kończak, 2024. "Kadec–Klee property with respect to the local convergence in measure of Orlicz–Lorentz spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 297(5), pages 1793-1817, May.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:5:p:1793-1817
    DOI: 10.1002/mana.202300151
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    References listed on IDEAS

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    1. Xiaoyan Li & Yunan Cui, 2022. "Strict convexity of Orlicz sequence spaces equipped with p-Amemiya norms," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(3), pages 660-671, September.
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