On normal partial isometries

Author:

Aouichaoui Mohamed Amine1ORCID

Affiliation:

1. Department of Mathematics, LR/18/ES/16: Analysis, Geometry and Applications , Monastir Preparatory Engineering Institute , 5019 Monastir , Tunisia

Abstract

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 ( ) {\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 ( ) {\mathcal{B}(\mathcal{H})} is similar to a normal partial isometry. We close the paper by treating when a partial isometry is hyponormal.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference19 articles.

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3. S. R. Caradus, Generalized Inverses and Operator Theory, Queen’s Papers Pure Appl. Math. 50, Queen’s University, Kingston, 1978.

4. J. B. Conway, A Course in Operator Theory, Grad. Stud. Math. 21, American Mathematical Society, Providence, 2000.

5. R. Doran, Characterizations of C * C^{*} -Algebras. The Gelfand–Naimark Theorems, CRC Press, Boca Raton, 2019.

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