On C-Normal Operator Matrices.

An operator T ∈ L (H) is said to be C-normal if there exists a conjugation C on H such that the commutator [ (C T) # , C T ] equals zero, where [ R , S ] : = R S - S R and R # is a Hermitian adjont operator of R as in (1). If there exists a conjugation C with respect to which T ∈ 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. [ABSTRACT FROM AUTHOR]