New results on semiclosedness with illustration of the solution of feedback control problems

We study in this paper the concept of closable-semiclosed operators in a Hilbert space and their algebraic and topological structures are investigated. We establish a non-trivial correspondence between closable and semiclosed operators. We also provide some necessary and/or sufficient conditions under which semiclosed operaors are closable. Interesting examples are provided and as an illustration, we investigate existence and uniqueness of solutions of feedback control problems where the characteristic operator is semiclosed.