On a trace formula for functions of noncommuting operators

2019/01/28 by А. Б. Александров, Aleksandrov, A. B., Vladimir Peller +3
Mathematics · #Spectral Theory in Mathematical Physics #advanced mathematical theories #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1901.09495

Abstract

The main result of the paper is that the Lifshits--Krein trace formula cannot be generalized to the case of functions of noncommuting self-adjoint operators. To prove this, we show that for pairs (A₁,B₁) and (A₂,B₂) of bounded self-adjoint operators with trace class differences A₂-A₁ and B₂-B₁, it is impossible to estimate the modulus of the trace of the difference f(A₂,B₂)-f(A₁,B₁) in terms of the norm of f in the Lipschitz class.

Related

• The Lifshits--Krein trace formula and operator Lipschitz functions
• Functions of triples of noncommuting self-adjoint operators and their perturbations
• Functions of perturbed noncommuting self-adjoint operators
• Trace formulae for perturbations of class \bs\bS_m
• Krein's trace formula for unitary operators and operator Lipschitz\n functions