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Author: search.filters.author.Naik, S.M.Subject: search.filters.subject.Schur complement

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    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.
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    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.