Functions of noncommuting operators under perturbation of class \boldsymbolS_p

2019/02/17 by Aleksandrov, Aleksei, Peller, Vladimir
#47A55 #47A60 47A55 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1902.06346

Abstract

In this article we prove that for p>2, there exist pairs of self-adjoint operators (A₁,B₁) and (A₂,B₂) and a function f on the real line in the homogeneous Besov class B_∞,1¹(\Bbb R²) such that the differences A₂-A₁ and B₂-B₁ belong to the Schatten--von Neumann class \boldsymbolS_p but f(A₂,B₂)-f(A₁,B₁)\not∈\boldsymbolS_p. A similar result holds for functions of contractions. We also obtain an analog of this result in the case of triples of self-adjoint operators for any p≥1

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• Functions of triples of noncommuting self-adjoint operators under perturbations of class \boldsymbol S_p
• Functions of perturbed noncommuting unbounded self-adjoint operators
• Functions of perturbed operators
• Functions of perturbed noncommuting self-adjoint operators
• Functions of triples of noncommuting self-adjoint operators and their perturbations