English

$C$-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 HH, we say that a bounded linear operator TT acting on HH is CC-normal, where CC is a conjugation on HH, if it satisfies CTTC=TTCT^*TC=TT^*. For a normal operator, we give geometric conditions which guarantee that its rank-one perturbation is a CC-normal for some conjugation CC.

Keywords

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}
}