$C$-normality of rank-one perturbations of normal operators
Functional Analysis
2022-04-12 v2 Operator Algebras
Spectral Theory
Abstract
For a separable complex Hilbert space , we say that a bounded linear operator acting on is -normal, where is a conjugation on , if it satisfies . For a normal operator, we give geometric conditions which guarantee that its rank-one perturbation is a -normal for some conjugation .
Cite
@article{arxiv.2202.00614,
title = {$C$-normality of rank-one perturbations of normal operators},
author = {Zouheir Amara and Mourad Oudghiri},
journal= {arXiv preprint arXiv:2202.00614},
year = {2022}
}