On C-hyponormal operators

A bounded linear operator T : H H is a C -hyponormal operator if T * T -CT T * C 0 for a conjugation C on H .In this paper, we study properties of C -hyponormal operators.Especially, we prove that for M Lat(T ) and a conjugationFinally, we prove that if T * is p -hyponormal for 0 < p 1 and C is a conjugation on H , then T is C -hyponormal if and only if T is normal.