The necessary and sufficient conditions for both the Kadec–Klee property as well as the Kadec–Klee property with respect to the coordinatewise convergence in Orlicz–Lorentz sequence spaces equipped with the Orlicz norm and generated by arbitrary Orlicz functions as well as any non-increasing weight sequences are given. Moreover, for their subspaces of elements with an order continuous norm the full characterization of the Kadec–Klee property with respect to the coordinatewise convergence is presented. Some tools useful in the proofs of the main results are also provided.

中文翻译：

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配备Orlicz范数的Orlicz-Lorentz序列空间的Kadec-Klee属性

关于Kadec–Klee属性以及Kadec–Klee属性的充要条件，这些条件取决于Orlicz-Lorentz序列空间的坐标收敛，该序列空间具有Orlicz范数并由任意Orlicz函数以及任何非递增函数生成给出了权重序列。此外，对于具有连续连续范数的元素的子空间，提出了Kadec–Klee属性相对于坐标收敛的完整特征。还提供了一些可用于证明主要结果的工具。