Linear Maps Preserving Idempotence on Nest Algebras  

作　　者：JianLianCUI JinChuanHOU 

机构地区：[1]SchoolofMathematicalSciences,PekingUniversity,Beijing100871,P.R.China [2]DepartmentofMathematics,ShanxiTeachersUniversity,Linfen041004,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2004年第5期807-820,共14页数学学报（英文版）

基　　金：supported by NNSFC(10071046);PNSFS(981009);PYSFS(20031009);China Postdoctoral Science Foundation

摘　　要：In this paper,we discuss the rank-1-preserving linear maps on nest algebras of Hilbert- space operators.We obtain several characterizations of such linear maps and apply them to show that a weakly continuous linear bijection on an atomic nest algebra is idempotent preserving if and only if it is a Jordan homomorphism,and in turn,if and only if it is an automorphism or an anti-automorphism.In this paper,we discuss the rank-1-preserving linear maps on nest algebras of Hilbert- space operators.We obtain several characterizations of such linear maps and apply them to show that a weakly continuous linear bijection on an atomic nest algebra is idempotent preserving if and only if it is a Jordan homomorphism,and in turn,if and only if it is an automorphism or an anti-automorphism.

关 键 词：Nest algebras Rank-1 operators Idempotent operators Jordan isomorphisms 

分 类 号：O151.21[理学—数学]