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., 2023, Volume 14, Number 3,Pages <nobr>8

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

S. K. Athira^a, K. Kamaraj^b, P. S. Johnson^a

^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

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.

MSC: 47A05, 15A09

Received: 25.01.2023

Language: English

DOI: 10.32523/2077-9879-2023-14-3-08-25