Invariance of Conjugate Normality Under Similarity (Communications in Mathematical Research, 2024)
An operator $T$ on a separable, infinite dimensional, complex Hilbertspace $\mathcal{H}$ 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 conjugatenormality 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 $(T−λ_1)(T−λ_2)=0.$