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.
基金
supported by NNSFC(10071046)
PNSFS(981009)
PYSFS(20031009)
China Postdoctoral Science Foundation
