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

A. B. Aleksandrov, V. V. Peller

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

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

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
Paper Structure (4 sections, 57 equations)

This paper contains 4 sections, 57 equations.

Table of Contents

  1. Introduction
  2. Double operator integrals and Schur multipliers
  3. The Besov class $\boldsymbol{B_{\infty,1}^1({\Bbb R}^2)}$
  4. The main result