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arXiv · 2202.00614

$C$-normality of rank-one perturbations of normal operators

Zouheir Amara·Mourad Oudghiri
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Abstract

For a separable complex Hilbert space $H$, we say that a bounded linear operator $T$ acting on $H$ is $C$-normal, where $C$ is a conjugation on $H$, if it satisfies $CT^*TC=TT^*$. For a normal operator, we give geometric conditions which guarantee that its rank-one perturbation is a $C$-normal for some conjugation $C$.

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Zouheir Amara, Mourad Oudghiri. 2022-01-31. $C$-normality of rank-one perturbations of normal operators. https://arxiv.org/abs/2202.00614

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