Remark on skew $m$-complex symmetric operators (Research on structure of operators using operator means and related topics)

Abstract

In this paper we study skew m-complex symmetric operators. In particular, we prove that if Tin mathcal{L}(mathcal{H}) is a skew m-complex symmetric operator with a conjugation C, then e^{itT}, e^{-itT}, and e^{-itT^{*}} are (m, C)-isometric for every tin mathbb{R}. Moreover, we investigate some conditions for skew m-complex symmetric operators to be skew (m-1)-complex symmetric.