Browsing by Author "Athira, S.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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    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.