Faculty Publications
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Publications by NITK Faculty
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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 New identity on Parseval p-approximate Schauder frames and applications(Taru Publications, 2021) Mahesh Krishna, K.; Johnson, P.A very useful identity for Parseval frames for Hilbert spaces was obtained by Balan, Casazza, Edidin, and Kutyniok. In this paper, we obtain a similar identity for Parseval p-approximate Schauder frames for Banach spaces which admits a homogeneous semi-inner product in the sense of Lumer-Giles. © 2021 Taru Publications.Item Convergence of complementable operators(Elsevier Inc., 2025) Naik, S.M.; Johnson, P.Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This paper focuses on the convergence properties of complementable operators, investigating when the limit of sequence of complementable operators remains complementable. We also explore the convergence of sequences and series of powers of complementable operators, providing new insights into their convergence behavior. Additionally, we examine the conditions under which the set of complementable operators is the subset of set of boundary points of the set of non-complementable operators with respect to the strong operator topology. The paper further explores the topological structure of the subset of complementable operators, offering a characterization of its closed subsets. © 2025 Elsevier Inc.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 Frame Scaling by Graphs(Indian National Science Academy, 2025) Ayyanar, K.; Johnson, P.; Senthil Thilak, A.S.In this paper, we investigate the scalability of a given frame in Rn by using graphs. For each frame ? in Rn, we associate a simple undirected graph G(?) and use it to verify the scalability of ?. We provide some necessary conditions to test the scalability of a given frame. Finally, we study the scalability of some special classes of frames by using graphs. © The Indian National Science Academy 2025.Item 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.Item Riesz Bases in Krein Spaces(Indian National Science Academy, 2025) Jahan, S.; Johnson, P.We start by introducing and studying the definition of a Riesz basis in a Krein space (K,[.,.]), along with a condition under which a Riesz basis becomes a Bessel sequence. The concept of biorthogonal sequence in Krein spaces is also introduced, providing an equivalent characterization of a Riesz basis. Additionally, we explore the concept of the Gram matrix, defined as the sum of a positive and a negative Gram matrices, and specify conditions under which the Gram matrix becomes bounded in Krein spaces. Further, we characterize the conditions under which the Gram matrices {[fn,fj]n,j?I+} and {[fn,fj]n,j?I-} become bounded invertible operators. Finally, we provide an equivalent characterization of a Riesz basis in terms of Gram matrices. © The Indian National Science Academy 2025.Item Complementable operators and their Schur complements(Indian National Science Academy, 2025) Naik, S.M.; Johnson, P.In this paper, we characterize complementable operators and provide more precise expressions for the Schur complement of these operators using a single Douglas solution. We demonstrate the existence of subspaces where the given operator is invariably complementable. Additionally, we investigate the range-Hermitian property of these operators. © The Indian National Science Academy 2025.Item MULTIPLIERS FOR LIPSCHITZ p?BESSEL SEQUENCES IN METRIC SPACES(Kyungnam University Press, 2025) Mahesh Krishna, K.; Johnson, P.; Harikrishnan, H.The notion of multipliers in Hilbert spaces was introduced by Schatten in 1960 using orthonormal sequences, and it was generalized by Balazs in 2007 using Bessel sequences. This concept was further extended to Banach spaces by Rahimi and Balazs in 2010 using p-Bessel sequences. In this paper, we extend this framework by considering Lipschitz functions. Along the way, we define frames for metric spaces, thereby generalizing the notion of frames and Bessel sequences for Banach spaces. We show that when the symbol sequence converges to zero, the associated multiplier is a Lipschitz compact operator. Finally, we study how variations in the parameters of the multiplier affect its properties. © 2025, Kyungnam University Press. All rights reserved.