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Author: search.filters.author.Johnson, P.S.Subject: search.filters.subject.Moore-Penrose inverse

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    Closed EP and hypo-EP operators on Hilbert spaces
    (Springer Science and Business Media B.V., 2022) Johnson, P.S.
    A bounded linear operator A on a Hilbert space H is said to be an EP (hypo-EP) operator if ranges of A and A∗ are equal (range of A is contained in range of A∗) and A has a closed range. In this paper, we define EP and hypo-EP operators for densely defined closed linear operators on Hilbert spaces and extend results from bounded linear operator settings to (possibly unbounded) closed linear operator settings. © 2022, The Author(s), under exclusive licence to The Forum D’Analystes.
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    Reverse order law for generalized inverses with indefinite Hermitian weights
    (University of Nis, 2023) Kamaraj, K.; Johnson, P.S.; Athira, S.K.
    In this paper, necessary and sufficient conditions are given for the existence of Moore-Penrose inverse of a product of two matrices in an indefinite inner product space (IIPS) in which reverse order law holds good. Rank equivalence formulas with respect to IIPS are provided and an open problem is given at the end. © 2023, University of Nis. All rights reserved.
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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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    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.