Reverse order law for Moore-Penrose inverse of closed operators and its applications

K Athira Satheesh (), P. Sam Johnson () and K. Kamaraj ()
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K Athira Satheesh: National Institute of Technology Karnataka (NITK)
P. Sam Johnson: National Institute of Technology Karnataka (NITK)
K. Kamaraj: University College of Engineering

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 1026-1035

Abstract: Abstract We present some results to characterize the reverse order law for Moore-Penrose inverse of closed densely defined operators on Hilbert spaces. We use the basic properties of the Moore-Penrose inverse of closed operators to prove our results. We provide an example to show that the reverse order law for Moore-Penrose inverse of unbounded closed densely defined operators may not hold good in general. We also provide a method to find the Moore-Penrose inverse of a closed densely defined operator as an application of the reverse order law using polar decomposition.

Keywords: Moore-Penrose inverse; Reverse order law; Closed densely defined operator; Polar decomposition; 47A05; 15A09 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-025-00818-1

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