Functions of commuting contractions under perturbation

2018/04/06 by Peller, Vladimir
#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.1804.02121

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, Hölder 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.

Related

• Functions of perturbed commuting dissipative operators
• Functions of perturbed pairs of noncommuting contractions
• Perturbations of operators similar to contractions and the commutator equation
• The behavior of functions of operators under perturbations
• Functions of noncommuting operators under perturbation of class \boldsymbolS_p