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

页码：4811 / 4818

页数：8

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