Faculty Publications

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    ALGEBRAIC PROOFS OF CHARACTERIZING REVERSE ORDER LAW FOR CLOSED RANGE OPERATORS IN HILBERT SPACES
    (L.N. Gumilyov Eurasian National University, 2023) Athira, S.K.; Kamaraj, K.; Johnson, P.S.
    We present more than 60 results, including some range inclusion results to characterize the reverse order law for the Moore-Penrose inverse of closed range Hilbert space operators. We use the basic properties of the Moore-Penrose inverse to prove the results. Some examples are also provided to illustrate failure cases of the reverse order law in an infinite-dimensional setting. © (2023). All Rights Reserved.
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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.