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 several interesting 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 $\mathcal{A}$ in order to have the Hyers-Ulam stability.

21 pages