Abstract
In this paper, we prove that every diagonal operator on a Hilbert space of which is of multiplicity one and has perfect spectrum admits a rank one perturbation without eigenvalues. This answers a question of Ionascu.
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Klaja, H. Rank One Perturbations of Diagonal Operators Without Eigenvalues. Integr. Equ. Oper. Theory 83, 429–445 (2015). https://doi.org/10.1007/s00020-015-2250-5
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DOI: https://doi.org/10.1007/s00020-015-2250-5