Functions of perturbed noncommuting unbounded self-adjoint operators

2021/09/06 by А. Б. Александров, Aleksandrov, Aleksei, Vladimir Peller +1
Mathematics · #Advanced Operator Algebra Research #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2109.02339

openalex publication_date 2021/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f be a function on \Bbb R² in the inhomogeneous Besov space B_∞,1¹(\Bbb R²). For a pair (A,B) of not necessarily bounded and not necessarily commuting self-adjoint operators, we define the function f(A,B) of A and B as a densely defined linear operator. We show that if 1≤ p≤2, (A₁,B₁) and (A₂,B₂) are pairs of not necessarily bounded and not necessarily commuting self-adjoint operators such that both A₁-A₂ and B₁-B₂ belong to the Schatten--von Neumann class \boldsymbolS_p and f is in the above inhomogeneous Besov space, then the following Lipschitz type estimate holds: ‖f(A₁,B₁)-f(A₂,B₂)‖_\boldsymbolS_p \leconstmax\‖A₁-A₂‖_\boldsymbolS_p,‖B₁-B₂‖_\boldsymbolS_p\.

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