TY - JOUR
T1 - Invariance of Conjugate Normality Under Similarity
AU - Wang , Cun
AU - Yu , Meng
AU - Liang , Minyi
JO - Communications in Mathematical Research 
VL - 3
SP - 245
EP - 260
PY - 2024
DA - 2024/09
SN - 40
DO - http://doi.org/10.4208/cmr.2024-0002
UR - https://global-sci.org/intro/article_detail/cmr/23411.html
KW - $C$-normal operators, complex symmetric operators, similarity.
AB - <p style="text-align: justify;">An operator $T$ on a separable, infinite dimensional, complex Hilbert
space $\mathcal{H}$ is called conjugate normal if $C|T|C = |T^∗|$ for some conjugate linear,
isometric involution $C$ on $\mathcal{H}.$ 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 numbers $λ_1$, $λ_2$ such that $(T−λ_1)(T−λ_2)=0.$</p>