On C-Normal Operator Matrices

Abstract

An operator T∈L(H) is said to be C-normal if there exists a conjugation C on 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∈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. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.