Izumino has discussed a sequence of closed range operators (Tn) that converges to a closed range operator T on a Hilbert space to establish the convergence of Tn† → 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 Tn and T such that T has a closed range whenever each Tn has a closed range. © 2019 Khayyam Journal of Mathematics.

Balaji S

Department of Instrumentation

School of Electrical Engineering

Vellore Campus

P.S. Johnson

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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Journal	Khayyam Journal of Mathematics
Publisher	Tusi Mathematical Research Group (TMRG)
ISSN	24234788