Peller's problem concerning Koplienko-Neidhardt trace formulae: the\n unitary case

2015/09/02 by Clément Coine, Christian Le Merdy, Coine, Clément +7
Mathematics · #47A55 #47A56 #47B10 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1509.00616

openalex publication_date 2015/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We prove the existence of a complex valued C²-function on the unit circle,\na unitary operator U and a self-adjoint operator Z in the Hilbert-Schmidt class\nS², such that the perturbated operator f(e^iZU)-f(U)\n-
fracddt
bigl(f(e^itZU)
bigr)
_{vert t=0} does not belong to the\nspace S¹ of trace class operators. This resolves a problem of Peller\nconcerning the validity of the Koplienko-Neidhardt trace formula for unitaries.\n

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