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

TL;DR

This paper introduces new assumptions and proofs for local form subordination conditions, enabling the demonstration of Riesz basis properties in perturbed self-adjoint operators even with slow or non-monotone decay.

Contribution

It provides a novel approach to establishing Riesz bases for perturbed operators without requiring power decay in the subordination condition.

Findings

Riesz basis property holds under relaxed decay conditions

New proof techniques accommodate non-monotone decay

Extends applicability to broader classes of operator perturbations

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.