Rank one perturbations of diagonal operators without eigenvalues

2015/06/20 by Hubert Klaja, Klaja, Hubert
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1506.06283

18 Pages

arxiv created 2015/06/20 · arxiv updated 2015/06/23

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.

Related

• Spectra of rank-one perturbations of self-adjoint operators
• Direct and inverse spectral problems for rank-one perturbations of\n self-adjoint operators
• Notes on Rank One Perturbed Resolvent. Perturbation of Isolated\n Eigenvalue
• Spectral theory of rank one perturbations of normal compact operators
• Every operator has almost-invariant subspaces