Functions of pairs of commuting self-adjoint operators under relatively bounded perturbations

TL;DR

This paper investigates how functions of pairs of commuting self-adjoint operators change under relatively bounded perturbations, extending previous single-operator results using double operator integrals.

Contribution

It introduces new results on the stability of functions of operator pairs under perturbations, generalizing earlier single-operator findings with advanced integral techniques.

Findings

Established bounds for functions of operator pairs under perturbations

Extended single-operator perturbation results to pairs of operators

Utilized double operator integrals as a key analytical tool

Abstract

We study the behaviour of functions of pairs of commuting self-adjoint operators under perturbations by relatively bounded operators. We obtain analogs of our earlier results for functions of a single self-adjoint operator under relatively bounded perturbations. The main tool is double operator integrals