On m -skew complex symmetric operators

In this paper, the definition of m -skew complex symmetric operators is introduced. Firstly, we prove that Δ − m ( T ) is complex symmetric with the conjugation C and give some properties of Δ − m ( T ) . Secondly, let T be m -skew complex symmetric with conjugation C , if n is odd, then T n is m -skew complex symmetric with conjugation C ; if n is even, with the assumption T ∗ C T C = C T C T ∗ , then T^n is m -complex symmetric with conjugation C . Finally, we give some properties of m -skew complex symmetric operators.