Trace formulas for S^p-perturbations and extension of Koplienko-Neidhardt trace formulas

2024/11/25 by Arup Chattopadhyay, Chattopadhyay, Arup, Clément Coine +5
Mathematics · Physics and Astronomy · #47A55 #47A56 #47B10 #47B49 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Nonlinear Waves and Solitons #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2411.16426

openalex publication_date 2024/11/25 · openalex created_date 2024/12/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we extend the class of admissible functions for the trace formula of the second order in the self-adjoint, unitary, and contraction cases for a perturbation in the Hilbert-Schmidt class S²(H) by assuming a certain factorization of the divided difference f^[2]. This class is the natural one to ensure that the second order Taylor remainder is a trace class operator. It encompasses all the classes of functions for which the trace formula was previously known. Secondly, for a Schatten S^p-perturbation, 1

Related

• Trace formulae for perturbations of class \bs\bS_m
• An extension of the Koplienko-Neidhardt trace formulae
• Koplienko-Neidhardt trace formula for unitaries - A new proof
• Koplienko Trace Formula
• Peller's problem concerning Koplienko-Neidhardt trace formulae: the\n unitary case