REFLEXIVITY FOR SPACES OF REGULAR OPERATORS ON BANACH LATTICES

被引：1
|
作者：
Li, Yongjin [1 ]
Bu, Qingying [2 ]
机构：
[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Peoples R China
[2] Univ Mississippi, Dept Math, University, MS 38677 USA
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2022年 / 150卷 / 11期
关键词：
TENSOR-PRODUCTS;
D O I：
10.1090/proc/16018
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that if Banach lattices E and F are reflexive and each positive linear operator from E to F is compact then L-r( E; F), the space of all regular linear operators from E to F, is reflexive. Conversely, if E* or F has the bounded regular approximation property then the reflexivity of L-r( E; F) implies that each positive linear operator from E to F is compact. Analogously we also study the reflexivity for the space of regular multilinear operators on Banach lattices.
引用
收藏
页码：4811 / 4818
页数：8
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