Theoretical analysis demonstrates Hyers-Ulam stability criteria for closable operators in Hilbert spaces, highlighting necessary and sufficient conditions for block matrix complements.
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 block matrix in order to have the Hyers–Ulam stability.
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Majumdar et al. (2024) studied this question.
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