摘要
本文主要讨论因子Ｖｏｎ Ｎｅｕｍａｎｎ代数中套子代数上的线性满等距和自伴导子．证明了因子Ｖｏｎ Ｎｅｕｍａｎｎ代数中套子代数上的每个线性满等距是同构乘酉算子或者是反同构乘酉算子；给出了其上自伴导子是内导子的条件并得到有限因子 Ｖｏｎ Ｎｅｕｍａｎｎ代数中套子代数上的每个自伴导子都是内导子．
In this paper isometries and hermitain deivations on nest subalgebras of factor Von Neumann algebras are discused. It is proved that every isometry is either an isomorphism multiply by a unitary operator or an anti-isomorphism multiply by a unitary operator. We give some conditions for which every hermitain derivation on nest subalgebras of factor Von Neumann algebras is inner, and show that every hermitain derivation on nest subalgebras of finite factor Von Neumann algebras is inner.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
1996年第1期64-70,共7页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目.
关键词
诺伊曼代数
套子代数
满等距
自伴导子
Von Neumann algebra, nest, nest subalgebra,isometry, hermitain derivation
