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Hyers–Ulam stability of unbounded closable operators in Hilbert spaces
(John Wiley and Sons Inc, 2024) Majumdar, A.; Johnson, P.S.; Mohapatra, R.N.
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 (Formula presented.) block matrix (Formula presented.) in order to have the Hyers–Ulam stability. © 2024 Wiley-VCH GmbH.
The Moore–Penrose inverses of unbounded closable operators and the direct sum of closed operators in Hilbert spaces
(Taylor and Francis Ltd., 2025) Majumdar, A.; Johnson, P.S.
In this paper, we present some interesting results to characterize the Moore–Penrose inverses of unbounded closable operators and after investigating the Moore–Penrose inverses of the direct sum of closed operators with closed ranges in Hilbert spaces, we establish (Formula presented.), where (Formula presented.) is the reduced minimum modulus of T. © 2024 Informa UK Limited, trading as Taylor & Francis Group.