Browsing by Author "Kamaraj, K."

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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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    Estimates of Norms on Krein Spaces
    (Austral Internet Publishing, 2020) Athira, S.K.; Johnson, P.S.; Kamaraj, K.
    Various norms can be defined on a Krein space by choosing different underlying fundamental decompositions. Some estimates of norms on Krein spaces are discussed and a few results in Bognar’s paper are generalized. © 2020. Austral Internet Publishing. All Rights Reserved.
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    Generalized principal pivot transform and its inheritance properties
    (Springer Science and Business Media B.V., 2022) Kamaraj, K.; Johnson, P.S.; Naik, S.M.
    In this paper, some more properties of the generalized principal pivot transform are derived. Necessary and sufficient conditions for the equality between Moore–Penrose inverse of a generalized principal pivot transform and its complementary generalized principal pivot transform are presented. It has been shown that the generalized principal pivot transform preserves the rank of the symmetric part of a given square matrix. These results appear to be more generalized than the existing ones. Inheritance properties of P†-matrix are also characterized for generalized principal pivot transform. © 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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    Reverse order law for Moore-Penrose inverse of closed operators and its applications
    (Indian National Science Academy, 2025) Satheesh, K.A.; Johnson, P.; Kamaraj, K.
    We present some results to characterize the reverse order law for Moore-Penrose inverse of closed densely defined operators on Hilbert spaces. We use the basic properties of the Moore-Penrose inverse of closed operators to prove our results. We provide an example to show that the reverse order law for Moore-Penrose inverse of unbounded closed densely defined operators may not hold good in general. We also provide a method to find the Moore-Penrose inverse of a closed densely defined operator as an application of the reverse order law using polar decomposition. © The Indian National Science Academy 2025.