关于二次Putnam-Fuglede定理(Ⅰ)

On the Second Degree Putnam Fuglede Theorem

中文关键词:  正规算子  广义导算子  幂零算子  二次Putnam－Fuglede定理

英文关键词:normal operator  generalized derivation  nilpotent operator  the second degree Putnam Fuglede theorem.

中文摘要:

      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．本文给出了在幂零算子扰动下及在一些非正常算子时的二次ＰＦ定理

英文摘要:

      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.