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Eurasian Mathematical Journal, 2023, Volume 14, Number 3, Pages 8–25
DOI: https://doi.org/10.32523/2077-9879-2023-14-3-08-25 (Mi emj474) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Algebraic proofs of characterizing reverse order law for closed range operators in Hilbert spaces

S. K. Athiraa, K. Kamarajb, P. S. Johnsona

a Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka (NITK), Surathkal, Mangaluru, 575 025, India
b Department of Mathematics, University College of Engineering, BIT Campus, Tiruchirappalli, 620 024, India
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DOI: https://doi.org/10.32523/2077-9879-2023-14-3-08-25
Abstract: We present more than 60 results, including some range inclusion results to characterize the reverse order law for the Moore–Penrose inverse of closed range Hilbert space operators. We use the basic properties of the Moore-Penrose inverse to prove the results. Some examples are also provided to illustrate failure cases of the reverse order law in an infinite-dimensional setting.
Keywords and phrases: Moore-Penrose inverse, reverse order law, closed range operator.
Funding agency Grant number
NBHM 02011/12/2023/NBHM(R.P)/R&D II/5947
National Institute of Technology Karnataka
The first author thanks the National Institute of Technology Karnataka (NITK), Surathkal, for the financial support. The present work of the third author was partially supported by the National Board for Higher Mathematics (NBHM), Ministry of Atomic Energy, Government of India (Reference Number: 02011/12/2023/NBHM(R.P)/R&D II/5947).
Received: 25.01.2023
Document Type: Article
MSC: 47A05, 15A09
Language: English
Citation: S. K. Athira, K. Kamaraj, P. S. Johnson, “Algebraic proofs of characterizing reverse order law for closed range operators in Hilbert spaces”, Eurasian Math. J., 14:3 (2023), 8–25
Citation in format AMSBIB
\Bibitem{AthKamJoh23}
\by S.~K.~Athira, K.~Kamaraj, P.~S.~Johnson
\paper Algebraic proofs of characterizing reverse order law for closed range operators in Hilbert spaces
\jour Eurasian Math. J.
\yr 2023
\vol 14
\issue 3
\pages 8--25
\mathnet{http://mi.mathnet.ru/emj474}
\crossref{https://doi.org/10.32523/2077-9879-2023-14-3-08-25}
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