Analytic operator Lipschitz functions in the disk and a trace formula for functions of contractions

2017/05/19 by Malamud, M. M., Neidhardt, H., Peller, V. V.
#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.1705.07225

Abstract

In this paper we prove that for an arbitrary pair \T₁,T₀\ of contractions on Hilbert space with trace class difference, there exists a function \boldsymbolξ in L¹(\Bbb T) (called a spectral shift function for the pair \T₁,T₀\ ) such that the trace formula trace(f(T₁)-f(T₀))=∫_{\Bbb T} f'(ζ)\boldsymbolξ(ζ) dζ) holds for an arbitrary operator Lipschitz function f analytic in the unit disk.

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