Hyers–Ulam stability of unbounded closable operators in Hilbert spaces

Abstract

In this paper, we discuss the Hyers–Ulam stability of closable (unbounded) operators with some examples. We also present results pertaining to the Hyers–Ulam stability of the sum and product of closable operators to have the Hyers–Ulam stability and the necessary and sufficient conditions of the Schur complement and the quadratic complement of $2\times 2$ block matrix $A$ in order to have the Hyers–Ulam stability.