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On normal partial isometries

  • Mohamed Amine Aouichaoui ORCID logo EMAIL logo
Published/Copyright: July 25, 2023
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Abstract

Our aim in this paper is to determine when a partially isometric matrix is normal. However, we do not restrict ourselves to the finite-dimensional case and we describe when a partial isometry in ( ) satisfies several strong and weak normal properties. In particular, we give elegant characterisations of normal partial isometries on infinite-dimensional Hilbert Spaces in terms of generalized inverses; we collect some spectral properties and explore when an operator in ( ) is similar to a normal partial isometry. We close the paper by treating when a partial isometry is hyponormal.

Acknowledgements

I would like express my thanks to Professor Skhiri Haïkel and Dr. Garbouj Zied who encouraged me to write this paper.

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Received: 2022-09-20
Accepted: 2023-05-10
Published Online: 2023-07-25
Published in Print: 2023-12-01

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