Faculty Publications
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Item Factorization of EP Operators in Krein Spaces(Springer, 2021) Vinoth, A.; Johnson, P.A closed range bounded operator on a Hilbert space is said to be an EP operator if the operator commutes with its Moore-Penrose inverse. In this paper, we characterize EP operators through factorization in the Krein space settings. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.Item Computing the Moore-Penrose inverse using its error bounds(Elsevier Inc. usjcs@elsevier.com, 2020) Stanimirovi?, P.S.; Roy, F.; Gupta, D.K.; Srivastava, S.A new iterative scheme for the computation of the Moore-Penrose generalized inverse of an arbitrary rectangular or singular complex matrix is proposed. The method uses appropriate error bounds and is applicable without restrictions on the rank of the matrix. But, it requires that the rank of the matrix is known in advance or computed beforehand. The method computes a sequence of monotonic inclusion interval matrices which contain the Moore-Penrose generalized inverse and converge to it. Successive interval matrices are constructed by using previous approximations generated from the hyperpower iterative method of an arbitrary order and appropriate error bounds of the Moore-Penrose inverse. A convergence theorem of the introduced method is established. Numerical examples involving randomly generated matrices are presented to demonstrate the efficacy of the proposed approach. The main property of our method is that the successive interval matrices are not defined using principles of interval arithmetic, but using accurately defined error bounds of the Moore-Penrose inverse. © 2019 Elsevier Inc.Item 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.Item 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.Item 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.Item 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.Item 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.Item Generalized Core-EP Inverse: Representational and Computational Aspects(Indian National Science Academy, 2025) Chowdhry, G.; Roy, F.This study obtains several representations and properties of the generalized core-EP inverse (GCEP inverse). A novel canonical representation of the generalized core-EP inverse is obtained using the singular value decomposition (SVD). To accomplish this, a canonical representation of the AT,S(2) is also obtained. Further, utilizing the full-rank decomposition of AT,S(2), some full-rank representations of the GCEP inverse are obtained, which in turn gives some new integral representations of the GCEP inverse. Additionally, algorithms and numerical examples are given using the representations obtained. Algorithms are implemented in Matlab R2024a, and it concluded that our algorithms are reliable and give more accurate results than the existing one in [1]. © The Indian National Science Academy 2025.