Some remarks about disjointly homogeneous symmetric spaces

被引:4
作者
Astashkin, Sergey V. [1 ]
机构
[1] Samara Natl Res Univ, Dept Math, Moskovskoye Shosse 34, Samara 443086, Russia
来源
REVISTA MATEMATICA COMPLUTENSE | 2019年 / 32卷 / 03期
关键词
Symmetric space; p-Disjointly homogeneous lattice; Restricted p-disjointly homogeneous lattice; Lions-Peetre interpolation space; Isomorphism; REARRANGEMENT-INVARIANT SPACES; BANACH-LATTICES;
D O I
10.1007/s13163-018-0289-y
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let 1 <= p < infinity. A symmetric space X on [0, 1] is said to be p-disjointly homogeneous (resp. restricted p-disjointly homogeneous) if every sequence of normalized pairwise disjoint functions from X (resp. characteristic functions) contains a subsequence equivalent in X to the unit vector basis of l(p). Answering a question posed in the paper (Hernandez et al. in Funct Approx 50(2): 215-232, 2014), we construct, for each 1 <= p < infinity, a restricted p-disjointly homogeneous symmetric space, which is not p-disjointly homogeneous. Moreover, we prove that the property of p-disjoint homogeneity is preserved under Banach isomorphisms.
引用
收藏
页码:823 / 835
页数:13
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