Algebraic Proofs of Characterizing Reverse Order Law for Closed Range Operators in Hilbert Spaces


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Authors

  • Satheesh Kakkadan Athira
  • Kaliappan Kamaraj
  • Packia Prakassh Raaj Sam Johnson

DOI:

https://doi.org/10.32523/2077-9879-2023-14-3-08-25

Keywords:

Moore-Penrose inverse, reverse order law, closed range operator

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.

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Published

2023-09-30

How to Cite

Athira, S. K., Kamaraj, K., & Sam Johnson, P. P. R. (2023). Algebraic Proofs of Characterizing Reverse Order Law for Closed Range Operators in Hilbert Spaces. Eurasian Mathematical Journal, 14(3), 08–25. https://doi.org/10.32523/2077-9879-2023-14-3-08-25

Issue

Vol. 14 No. 3 (2023)

Section

Articles