Kadec-Klee properties of Orlicz-Lorentz sequence spaces equipped with the Orlicz norm

被引：2
|
作者：
Cui, Yunan [1 ]
Foralewski, Pawel [2 ]
Hudzik, Henryk [2 ,3 ]
Kaczmarek, Radoslaw [2 ]
机构：
[1] Harbin Univ Sci & Technol, Dept Math, Harbin 150080, Peoples R China
[2] Adam Mickiewicz Univ, Fac Math & Comp Sci, Uniwersytetu Poznanskiego 4, PL-61614 Poznan, Poland
[3] State Univ Appl Sci Plock, Fac Econ & Informat Technol, Ul Galczynskiego 28, PL-09400 Plock, Poland
来源：
POSITIVITY | 2021年 / 25卷 / 04期
关键词：
Orlicz– Lorentz sequence spaces; Subspace of order continuous elements; Orlicz norm; Kadec– Klee property; Klee property with respect to the coordinatewise convergence;
D O I：
10.1007/s11117-020-00803-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：1273 / 1294
页数：22
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