Invariance of Conjugate Normality Under Similarity

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 numbers λ 1 , λ 2 such that (T-λ 1 )(T-λ 2 ) = 0.