幂零算子的Jordan模型  

The Jordan Model of Nipotent Operator

作　　者：邹承祖[1] 

机构地区：[1]吉林大学数学系

出　　处：《吉林大学自然科学学报》1992年第3期31-36,共6页Acta Scientiarum Naturalium Universitatis Jilinensis

摘　　要：本文主要证明:(1)Hilbert空间上的幂零算子,在直和意义下,存在约化子空间;(2)Hilbert空间上的幂零算子存在一个稠的不变流形,使得幂零算子在其上限制是Jordan算子。这是有限维空间Jordan定理的推广,亦是Apostol,Douglas及Foias定理的推广。The present paper proves: (1) For each nilpotent operator on Hilbert space there exists a reducible subspace in the sense of the direct sum; (2) For every nilpotent operator on Hilbert space there exits a dense invariant manifold which makes the restrictive operator of the nilpotent operator on the dense invariant manifold is the Jordan operator. This is a straight extension of the Jordan theorem on finite dimensioral space.

关 键 词：幂零算子 Jordan模型 拟相似 

分 类 号：O177.1[理学—数学]