On C-Normal Operator Matrices

An operator \(T\in {\mathcal {L(H)}}\) is said to be C-normal if there exists a conjugation C on \({{\mathcal {H}}}\) such that the commutator \([(CT)^{\#}, CT]\) equals zero, where \([R,S]:=RS-SR\) and \(R^{\#}\) is a Hermitian adjont operator of R as in (1). If there exists a conjugation C with respect to which \(T\in \mathcal {L(H)}\) is C-normal, then T is called a conjugation-normal operator. In this paper, we study properties of conjugation-normal operator matrices. In particular, we focus on the conjugation-normality of the component operators of operator matrices which are conjugation-normal.