$C$-normality of rank-one perturbations of normal operators

Zouheir Amara, Mourad Oudghiri

For a separable complex Hilbert space $H$, we say that a bounded linear operator $T$ acting on $H$ is $C$-normal, where $C$ is a conjugation on $H$, if it satisfies $C{T}^{\ast }TC=T{T}^{\ast }$.…