On m-Complex Symmetric Operators

Abstract

In this paper, we study the spectral properties of m-complex symmetric operators. In particular, we prove that if T is m-complex symmetric with conjugation C, then T (n) is also m-complex symmetric with conjugation C for any . Moreover, if T is m-complex symmetric with conjugation C, then T is decomposable if and only if has the property (). As some applications, we give several examples of m-complex symmetric operators with conjugation C.