关于二次Putnam-Fuglede定理(Ⅰ)  

On the Second Degree Putnam Fuglede Theorem

作　　者：陈寅[1] 

机构地区：[1]河海大学数理系

出　　处：《Journal of Mathematical Research with Applications》1999年第S1期84-88,共5页数学研究及应用（英文版）

摘　　要：设Ｎ为正规算子，若Ｎ与交换子ＮＸ－ＸＮ可交换，则Ｎ必与Ｘ可交换，称此结论为二次Ｐｕｔｎａｍ－Ｆｕｇｌｅｄｅ定理．If N is a normal operator which commutes with the commutator NX-XN , then N commutes with X . This theorem is called the second degree Putnam Fuglede theorem. In this paper, we shall obtain some sufficient and necessary conditions for the second degree Putnam Fuglede theorem to be true under the perturbation of the nilpotent operators and for some non normal operators.

关 键 词：正规算子 广义导算子 幂零算子 二次Putnam-Fuglede定理 

分 类 号：O177.1[理学—数学]