Functions of compact operators under trace class perturbations

2024/02/15 by А. Александров, Aleksandrov, A. B., Vladimir Peller +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Stability and Controllability of Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2402.09843

Abstract

The paper studies the problem, for which continuous functions f on the real line \Bbb R, the difference of the functions f(B)-f(A) of self-adjoint operators A and B with trace class difference must also be of trace class. The main result of the paper shows that this happens if and only if the function f is operator Lipschitz on a neighbourhood of zero.

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