Functions of triples of noncommuting self-adjoint operators and their perturbations

TL;DR

This paper investigates the behavior of functions of triples of noncommuting self-adjoint operators, revealing that Lipschitz estimates in the trace norm do not hold for certain classes of functions, unlike the case for pairs of operators.

Contribution

It demonstrates the failure of Lipschitz type estimates in the trace norm for functions of triples of noncommuting self-adjoint operators within specific function classes.

Findings

Lipschitz estimates fail for functions of triples of operators

Contrast with the case of pairs of operators

Highlights limitations in perturbation theory for noncommuting triples

Abstract

In this paper we study properties of functions of triples of not necessarily commuting self-adjoint operators. The main result of the paper shows that unlike in the case of functions of pairs of self-adjoint operators there is no Lipschitz type estimates in the trace norm for arbitrary functions in the Besov class $B_{\infty,1}^1({\Bbb R}^3)$.