Johnson, P.S.Balaji, S.2026-02-052019Khayyam Journal of Mathematics, 2019, 5, 2, pp. 132-138https://doi.org/10.22034/kjm.2019.88428https://idr.nitk.ac.in/handle/123456789/24781Izumino has discussed a sequence of closed range operators (T<inf>n</inf>) that converges to a closed range operator T on a Hilbert space to establish the convergence of T<inf>n</inf>† ? T† for Moore-Penrose inverses. In general, if Tn ? T uniformly and each Tn has a closed range, then T need not have a closed range. Some sufficient conditions have been discussed on T<inf>n</inf> and T such that T has a closed range whenever each T<inf>n</inf> has a closed range. © 2019 Khayyam Journal of Mathematics.Closed range operatorsFrechet spacesMoore-Penrose inverses