ON OPERATORS T COMMUTING WITH CTC WHERE C IS A CONJUGATION

Abstract

In this paper, we study the properties of T satisfying [CTC, T] = 0 for some conjugation C where [R, S] := RS - SR: In particular, we show that if T is normal, then [CTC, C] = 0. Moreover, the class of operators T satisfy [CTC, T] = 0 is norm closed. Finally, we prove that if T is complex symmetric, then T is binormal if and only if [C vertical bar T vertical bar C, vertical bar T vertical bar] = 0.