Abstract
In this paper, we obtain some properties of (alpha, beta)-normal and we prove following assertions.
(i) If T is (alpha, beta)-normal operator, S is an invertible operator and X is a Hilbert-Schmidt operator such that T X = XS, then T * X = XS*.
(ii) If T is totally (alpha, beta)-normal operator, then the range of generalized derivation delta(T) : B(H) is an element of X -> TX - XT is an element of B(H) is orthogonal to its kernel.