Functions of commuting contractions under perturbation

TL;DR

This paper develops estimates for how functions of commuting contractions on Hilbert space change under perturbations, extending known results to broader classes of operators with various types of bounds.

Contribution

It provides new Lipschitz, Hölder, and Schatten-von Neumann estimates for functions of commuting contractions, generalizing previous results for other operator classes.

Findings

Established Lipschitz estimates for functions of commuting contractions.

Derived Hölder type bounds under perturbations.

Extended Schatten-von Neumann estimates to this operator class.

Abstract

The purpose of the paper is to obtain estimates for differences of functions of two pairs of commuting contractions on Hilbert space. In particular, Lipschitz type estimates, H\"older type estimates, Schatten--von Neumann estimates are obtained. The results generalize earlier known results for functions of self-adjoint operators, normal operators, contractions and dissipative operators.