Completeness of rank one perturbations of normal operators with lacunary spectrum

Anton Baranov
Saint Petersburg State University, Russia

Date(s) : 06/06/2016   iCal
10 h 00 min - 11 h 00 min

Suppose A is a compact normal operator on a Hilbert space H with certain lacunarity condition on the spectrum (which means, in particular, that its eigenvaluesgo to zero exponentially fast), and let L be its rank one perturbation. We show that either infinitely many moment equalities hold or the linear span of root vectors of L, corresponding to non-zero eigenvalues, is of finite codimension in H. In contrast to classical results, we do not assume the perturbation to be weak.


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