On C-quasinormal operators

Abstract

An operator T∈L(H) is called conjugation-quasinormal if there is a conjugation C on an infinite-dimensional complex Hilbert space H such that [CT,T∗T]=0 where [R,S]:=RS-SR. In particular, if such a conjugation C is specified, an operator T is said to be C-quasinormal. In this paper, we study various properties of conjugation-quasinormal operators. Especially, we provide several characterizations of conjugation-quasinormal operators. Moreover, if T is a partial isometry, we show that T is C-hyponormal if and only if T is C-quasinormal. Finally, we consider conjugation-operator transforms. © Tusi Mathematical Research Group (TMRG) 2025.