Properties of m-complex symmetric operators

Abstract

In this paper, we study several properties of m-complex symmetric operators. In particular, we prove that if T ε L(H) is an m-complex symmetric operator and N is a nilpotent operator of order n > 2 with TN = NT, then T + N is a (2n+m-2)-complex symmetric operator. Moreover, we investigate the decomposability of T+A and TA where T is an m-complex symmetric operator and A is an algebraic operator. Finally, we provide various spectral relations of such operators. As some applications of these results, we discuss Weyl type theorems for such operators.