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
相关论文
共 50 条
  • [41] Trigonometric series in the Orlicz-Lorentz spaces
    V. B. Simonov
    [J]. Russian Mathematics, 2007, 51 (6) : 61 - 74
  • [42] M-IDEAL PROPERTIES IN ORLICZ-LORENTZ SPACES
    Kaminska, Anna
    Lee, Han Ju
    Tag, Hyung-Joon
    [J]. HOUSTON JOURNAL OF MATHEMATICS, 2019, 45 (01): : 213 - 232
  • [43] Some Rotundities of Orlicz-Lorentz Spaces
    Gong, Wan Zhong
    Wang, Peng
    [J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2024, 40 (08) : 1893 - 1919
  • [44] Geometric properties of symmetric spaces with applications to Orlicz-Lorentz spaces
    Cerda, J
    Hudzik, H
    Kaminska, A
    Mastylo, M
    [J]. POSITIVITY, 1998, 2 (04) : 311 - 337
  • [45] Daugavet and diameter two properties in Orlicz-Lorentz spaces
    Kaminska, Anna
    Lee, Han Ju
    Tag, Hyung-Joon
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 529 (02)
  • [46] The Banach-Saks Properties in Orlicz-Lorentz Spaces
    Kaminska, Anna
    Lee, Han Ju
    [J]. ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [47] Orlicz-Lorentz spaces and their multiplication operators
    Erlin Castillo, Rene
    Camilo Chaparro, Hector
    Ramos Fernandez, Julio Cesar
    [J]. HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2015, 44 (05): : 991 - 1009
  • [48] Trigonometric Series in the Orlicz-Lorentz Spaces
    Simonov, V. B.
    [J]. RUSSIAN MATHEMATICS, 2007, 51 (06) : 61 - 74
  • [49] On Disjointly Homogeneous Orlicz-Lorentz Spaces
    Astashkin, S., V
    Strakhov, S., I
    [J]. MATHEMATICAL NOTES, 2020, 108 (5-6) : 631 - 642
  • [50] Isomorphic lp-subspaces in orlicz-lorentz sequence spaces
    Kaminska, A
    Raynaud, Y
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 134 (08) : 2317 - 2327
12345