Completeness of rank one perturbations of normal operators with lacunary spectrum
Completeness of rank one perturbations of normal operators with lacunary spectrum
Suppose \mathcal A is a compact normal operator on a Hilbert space H with certain lacunarity condition on the spectrum (which means, in particular, that its eigenvalues go to zero exponentially fast), and let \mathcal L be its rank one perturbation. We show that either infinitely many moment equalities hold …