Naik, S.M.Johnson, P.2026-02-032025Indian Journal of Pure and Applied Mathematics, 2025, 56, 3, pp. 1131-1143195588https://doi.org/10.1007/s13226-025-00828-zhttps://idr.nitk.ac.in/handle/123456789/20103In 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.Complementable operatorsSchur complementWeakly complementable operators