Local form subordination without a power decay and a criterion of Riesz basesness

Abstract

We revisit the local form subordination condition on the perturbation of a self-adjoint operators with compact resolvent, which is used to show the Riesz basis property of the eigensystem of the perturbed operator. Our new assumptions and new proof allow for establishing the Riesz basis property also in the case of slow and non-monotone decay in this subordination condition.