A Theoretical Study On Adjoint Drazin Inverse Hyponormal Operators Based On Fuzzy Soft Set Theory

Background: The aim of this article is to introduce novel traits of a new version of the fuzzy soft hyponormal operator which namely the fuzzy soft adjoint Drazin inverse hyponormal operator symbolized by (FS-(D, )- hyponormal operator),  in a fuzzy soft Hilbert space
Materials and Methods: this study in the realm of Operator Theory related to Fuzzy Soft Theory (FST). Some analytical properties have been discovered via theorems related in this concept, moreover submitted the conditions required to prove the direct sum and tensor produced.
Results: In this paper, a new class of fuzzy soft hyponormal operators, which is closely related to the Drazin inverse is introduced, namely the fuzzy soft adjoint Drazin inverse hyponormal operator. The necessary conditions for a new operator are investigated. The direct sum and tensor product are also examined
Conclusion: In this work, we obtain significant results based on the newly introduced definition fuzzy soft (D, )-hyponormal operator, such as a theorem equivalent to the definition under certain conditions as well as the sum and product of two operators.