Browsing by Author "Majumdar, A."

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    A-approximate point spectrum of A-bounded operators in semi-Hilbertian spaces
    (Indian National Science Academy, 2025) Majumdar, A.; Johnson, P.
    The paper delves into several characterizations of A-approximate point spectrum of A-bounded operators acting on a complex semi-Hilbertian space H and also investigates properties of the A-approximate point spectrum for the tensor product of two A12-adjoint operators. Furthermore, several properties of A-normal operators have been established. © The Indian National Science Academy 2025.
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    Hyers-Ulam stability of closed linear relations in Hilbert spaces
    (University of Nis, 2025) Majumdar, A.
    This paper introduces the concept of Hyers-Ulam stability for linear relations in normed linear spaces and presents several intriguing results that characterize the Hyers-Ulam stability of closed linear relations in Hilbert spaces. Additionally, sufficient conditions are established under which the sum and product of two Hyers-Ulam stable linear relations remain Hyers-Ulam stable. © 2025, University of Nis. 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.
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    On the generalized Cauchy dual of closed operators in Hilbert spaces
    (Springer Nature, 2025) Majumdar, A.; Johnson, P.S.; N Mohapatra, R.
    In this paper, we introduce the generalized Cauchy dual w(T)=T(T?T)† of a closed operator T with a closed range between Hilbert spaces and present intriguing findings that characterize the Cauchy dual of T. Additionally, we establish the result w(Tn)=(w(T))n, for all n?N, where T is a quasinormal EP operator. © The Author(s), under exclusive licence to University of Szeged 2025.
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    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.