On operators $T$ commuting with $CTC$\\ where $C$ is a conjugation
Bull. Korean Math. Soc.
Published online October 21, 2019
Muneo Ch\=o Cho, Eungil Ko, and Ji Eun Lee
Kanagawa University, Ewha Womans University, Sejong University, Seoul
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 $[C|T|C,|T|]=0$.
Keywords : conjugation operator; complex symmetric operator; normal operator
MSC numbers : Primary 47A05, Secondary 47B20.
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