Remark on Regularity of Continuous Operators on AL-Spaces  

作　　者：冯勋省 陈滋利 

机构地区：[1]Department of Applied Mathematics

出　　处：《Journal of Southwest Jiaotong University(English Edition)》2004年第1期79-82,共4页西南交通大学学报（英文版）

摘　　要：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.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.

关 键 词：Banach lattice AL-space AM-space ATOMICITY REGULARITY 

分 类 号：O177[理学—数学]