Abstract
A bounded linear operator A on a Hilbert space \({\mathcal {H}}\) is said to be an EP (hypo-EP) operator if ranges of A and \(A^*\) are equal (range of A is contained in range of \(A^*\)) and A has a closed range. In this paper, we define EP and hypo-EP operators for densely defined closed linear operators on Hilbert spaces and extend results from bounded linear operator settings to (possibly unbounded) closed linear operator settings.
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Acknowledgements
The author is thankful to Prof. M. Thamban Nair for having some discussion while preparing the manuscript and also for providing the proof for Theorem 2.13. He would like to thank the two referees for their constructive comments and suggestions, and especially one of them for entreating the author to add examples to illustrate Theorem 4.1.
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Communicated by Samy Ponnusamy.
Dedicated to Professor C. Ganesa Moorthy on his 60th birthday.
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Johnson, P.S. Closed EP and hypo-EP operators on Hilbert spaces. J Anal 30, 1377–1390 (2022). https://doi.org/10.1007/s41478-022-00401-5
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DOI: https://doi.org/10.1007/s41478-022-00401-5