On normal partial isometries
Mohamed Amine Aouichaoui · Georgian Mathematical Journal · 2023
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 ℬ ( ℋ ) {\mathcal{B}(\mathcal{H})} 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 ℬ ( ℋ ) {\mathcal{B}(\mathcal{H})} is similar to a normal partial isometry. We close the paper by treating when a partial isometry is hyponormal.