The class of D(T)–operators on Hilbert space

The purpose of this paper is to introduce a new class operator on separable Hilbert space. The operator T ∈ B(H) is called D(T)-operator if there exist U ∈ B(H), U≠۰, I such that T*TU = UT*T, where T* adjoint operator of T. Then, some main properties of the class of D(T)-operator are studied in this research.