Invariance of Conjugate Normality Under Similarity  

作　　者：Cun Wang Meng Yu Minyi Liang 

机构地区：[1]School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 102488,P.R.China [2]School of Mathematics,Jilin University,Changchun,jilin 130012,P.R.China

出　　处：《Communications in Mathematical Research》2024年第3期245-260,共16页数学研究通讯（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No.12171195).

摘　　要：An operator T on a separable,infinite dimensional,complex Hilbert space H is called conjugate normal if C|T|C=|T^(*)| for some conjugate linear,isometric involution C on H.This paper focuses on the invariance of conjugate normality under similarity.Given an operator T,we prove that every operator A similar to T is conjugate normal if and only if there exist complex numbersλ_(1),λ_(2)such that(T-λ_(1))(T-λ_(2))=0.

关 键 词：C-normal operators complex symmetric operators SIMILARITY 

分 类 号：O17[理学—数学]