Skew m-Complex Symmetric Operators

Abstract

In this paper we study skew m-complex symmetric operators. In particular, we show that if T is an element of L(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 t is an element of R. Moreover, we examine some conditions for skew m-complex symmetric operators to be skew (m - 1)-complex symmetric.