Abstract
The class of D(T)- operators are equivalent to the class of quasi-normal operators. This paper discusses additional properties of this class of operators. Assuming that if the operator T is not far from normality and U serves as an interrupter, it follows that the operator U will be both unique and positive. Moreover, we explore other properties that merge when the operator T commutes with T^* T. In one of our main theorems, we demonstrate that the operator T in the class D(T) is also normal when it is invertible.
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