Other Properties of the Class D(T)

Author:

Shawkat ShaymaaORCID

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.

Publisher

University of Kufa

Reference8 articles.

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2. Conway, J., A Course in Functional Analysis, Springer Verlag. New York, 1985. https://doi.org/10.1007/978-1-4757-

3. Elaf, S.A., The Class of D(T)-operators on Hilbert Spaces, Int. J. Nonlinear Anal. Appl, 12(2021), 1293-1298.

4. Halmos, P.R., A Hilbert Space Problem Book, Springer Verlag. New York, 1982. https://doi.org/10.1007/978-1-4684-

5. Istratescu, V., Introduction to Linear Operator Theory, Marcel Dekker, INC. New York, and Basel, 1981. ttps://www.taylorfran cis.com/books/mono/10.1201/9781003065050/introduction-linear-operator-theory-vasile-istratescu.

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