Non-squareness properties of Orlicz–Lorentz sequence spaces☆
Non-squareness properties of Orlicz–Lorentz sequence spaces☆
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DOI：
10.1016/j.jfa.2012.10.014
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发表时间：
2013-01
影响因子：
1.7
通讯作者：
P. Foralewski;H. Hudzik;P. Kolwicz
中科院分区：
文献类型：
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作者：
P. Foralewski;H. Hudzik;P. Kolwicz
本文给出了Orlicz-Lorentz序列空间λφ，ω及其n维子空间λφ，ωn（n大于等于2）以及λφ，ω中所有阶连续元素的子空间[公式：见文本]的非平方性（非平方性，局部一致非平方性和一致非平方性）的准则。由于还允许简并Orlicz函数φ和简并权序列ω，这些研究涉及到最可能广泛的Orlicz - lorentz序列空间。最后，作为直接结果，导出了Orlicz序列空间所有非平方性的准则，这些准则完成了Sundaresan (1966) [53], Hudzik (1985) [23], Hudzik(1985)[24]的结果。值得回顾的是，均匀非方形是一个重要的性质，因为它意味着超自反性以及不动点性质(参见James (1964) [31], James（1972)[33]和García-Falset等人（2006）[19]）。
In this paper criteria for non-squareness properties (non-squareness, local uniform non-squareness and uniform non-squareness) of Orlicz–Lorentz sequence spaces λφ,ωand of their n-dimensional subspaces λφ,ωn(n⩾2) as well as of the subspaces [Formula: see text] of all order continuous elements in λφ,ωare given. Since degenerate Orlicz functions φ and degenerate weight sequences ω are also admitted, these investigations concern the most possible wide class of Orlicz–Lorentz sequence spaces. Finally, as immediate consequences, criteria for all non-squareness properties of Orlicz sequence spaces, which complete the results of Sundaresan (1966) [53], Hudzik (1985) [23], Hudzik (1985) [24], are deduced. It is worth recalling that uniform non-squareness is an important property, because it implies super-reflexivity as well as the fixed point property (see James (1964) [31], James (1972) [33] and García-Falset et al. (2006) [19]).