Neutrosophic Adjoint, Self-Adjoint, and Unitary Operators on Neutrosophic Hilbert Spaces

Source abstract

In this paper, we introduce new definitions of neutrosophic adjoint, self-adjoint, and unitary operators acting on a neutrosophic Hilbert space. Fundamental properties are established, and several key results are proved to characterize the behavior of these operators within the neutrosophic framework. It is further shown that operators on neutrosophic Hilbert spaces generalize their classical counterparts, with classical operators on Hilbert spaces recovered as a special case when the truth-membership degree is equal to 1 and both the indeterminacy-membership and falsity-membership degrees are equal to 0. Moreover, the paper presents a rigorous analytical study of the structural and functional properties of neutrosophic operators, thereby contributing to the advancement of operator theory on neutrosophic Hilbert spaces.