Skew $m$-complex symmetric operators

Abstract

In this paper we study skew $m$-complex symmetric operators. In particular, we show that if $T\in{\cal{L}}({\cal{H}})$ is a skew $m$-complex symmetric operator with a conjugation $C$, then $e^{itT}$, $e^{-itT}$, and $e^{-it{T}^{\ast}}$ are $(m,C)$-isometric for every $t \in \R$. Moreover, we examine some conditions for skew $m$-complex symmetric operators to be skew $(m-1)$-complex symmetric.