Higher order \Sc²-differentiability and application to Koplienko trace formula

2017/12/29 by Clément Coine, Christian Le Merdy, Coine, Clément +5
Mathematics · #46L52 #47A55 #47B49 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1712.10289

openalex publication_date 2017/12/29 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

Let A be a selfadjoint operator in a separable Hilbert space, K a selfadjoint Hilbert-Schmidt operator, and f∈ Cⁿ(ℝ). We establish that φ(t)=f(A+tK)-f(A) is n-times continuously differentiable on ℝ in the Hilbert-Schmidt norm, provided either A is bounded or the derivatives f⁽ⁱ⁾, i=1,…,n, are bounded. As an application of the second order \Sc²-differentiability, we extend the Koplienko trace formula from the Besov class B_∞1²(\R) to functions f for which the divided difference f^[2] admits a certain Hilbert space factorization.

Citations

• Operator Lipschitz functions (English translation)

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