西南交通大学学报(英文版)
西南交通大學學報(英文版)
서남교통대학학보(영문판)
JOURNAL OF SOUTHWEST JIAOTONG UNIVERSITY
2004年
1期
79-82
,共4页
Banach lattice%AL-space%AM-space%Atomicity%Regularity
Let E and F be Banach lattices. It is known that if every continuous linear operator from E into F is regular, then, under some mild assumptions on E or F, either E is lattice isomorphic to an AL-space or F is lattice isomorphic to an AM-space. Here we present a characterization on an AL-space E such that every bounded linear operator from E into a Banach lattice is regular. A counterexample is also provided, which shows that the results are unexpected even if the domain is an AL-space or the range space is an AM-space.
