Some Properties of D-Operator on Hilbert Space
Keywords:Hilbert space, Drazin operator, Normal operator, D-normal operator, n-normal operator, class (Q) operators
In this paper, we introduce a new type of Drazin invertible operator on Hilbert spaces, which is called D-operator. Then, some properties of the class of D-operators are studied. We prove that the D-operator preserves the scalar product, the unitary equivalent property, the product and sum of two D-operators are not D-operator in general but the direct product and tenser product is also D-operator.