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Relatively bounded and relatively trace class perturbations. / Aleksandrov, A.B.; Peller, V.V.

In: Comptes Rendus Mathematique, Vol. 363, 2025, p. 377-382.

Research output: Contribution to journal › Article › peer-review

Harvard

Aleksandrov, AB & Peller, VV 2025, 'Relatively bounded and relatively trace class perturbations', Comptes Rendus Mathematique, vol. 363, pp. 377-382. https://doi.org/10.5802/crmath.722

APA

Aleksandrov, A. B., & Peller, V. V. (2025). Relatively bounded and relatively trace class perturbations. Comptes Rendus Mathematique, 363, 377-382. https://doi.org/10.5802/crmath.722

Vancouver

Aleksandrov AB, Peller VV. Relatively bounded and relatively trace class perturbations. Comptes Rendus Mathematique. 2025;363:377-382. https://doi.org/10.5802/crmath.722

Author

Aleksandrov, A.B. ; Peller, V.V. / Relatively bounded and relatively trace class perturbations. In: Comptes Rendus Mathematique. 2025 ; Vol. 363. pp. 377-382.

BibTeX

@article{bdb3450ba14046399db7eab11f96788c,
title = "Relatively bounded and relatively trace class perturbations",
abstract = "In this note we study the behaviour of functions of self-adjoint operators under relatively bounded and relatively trace class perturbations. We introduce and study the class of relatively operator Lipschitz functions. We obtain a trace formula in the case of relatively trace class perturbations and show that this class of functions is the maximal class of functions for which the trace formula holds. Our method also gives us a new approach to the inequality R |ξ(t )|(1 + |t |)−1 dt < ∞ for the spectral shift function ξ in the case of relatively trace class perturbations. {\textcopyright} 2025 Academie des sciences. All rights reserved.",
keywords = "double operator integrals, Relatively bounded perturbation, relatively operator Lipschitz class, relatively trace class perturbation, self-adjoint operators, trace formula",
author = "A.B. Aleksandrov and V.V. Peller",
note = "Export Date: 05 February 2026; Cited By: 0",
year = "2025",
doi = "10.5802/crmath.722",
language = "Английский",
volume = "363",
pages = "377--382",
journal = "Comptes Rendus Mathematique",
issn = "1631-073X",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Relatively bounded and relatively trace class perturbations

AU - Aleksandrov, A.B.

AU - Peller, V.V.

N1 - Export Date: 05 February 2026; Cited By: 0

PY - 2025

Y1 - 2025

N2 - In this note we study the behaviour of functions of self-adjoint operators under relatively bounded and relatively trace class perturbations. We introduce and study the class of relatively operator Lipschitz functions. We obtain a trace formula in the case of relatively trace class perturbations and show that this class of functions is the maximal class of functions for which the trace formula holds. Our method also gives us a new approach to the inequality R |ξ(t )|(1 + |t |)−1 dt < ∞ for the spectral shift function ξ in the case of relatively trace class perturbations. © 2025 Academie des sciences. All rights reserved.

AB - In this note we study the behaviour of functions of self-adjoint operators under relatively bounded and relatively trace class perturbations. We introduce and study the class of relatively operator Lipschitz functions. We obtain a trace formula in the case of relatively trace class perturbations and show that this class of functions is the maximal class of functions for which the trace formula holds. Our method also gives us a new approach to the inequality R |ξ(t )|(1 + |t |)−1 dt < ∞ for the spectral shift function ξ in the case of relatively trace class perturbations. © 2025 Academie des sciences. All rights reserved.

KW - double operator integrals

KW - Relatively bounded perturbation

KW - relatively operator Lipschitz class

KW - relatively trace class perturbation

KW - self-adjoint operators

KW - trace formula

U2 - 10.5802/crmath.722

DO - 10.5802/crmath.722

M3 - статья

VL - 363

SP - 377

EP - 382

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

ER -

ID: 149073302