Geodesic
Formula of the regularized trace for perturbation in the Schatten--von Neumann of discrete operators
Ufa mathematical journal, Tome 7 (2015) no. 4, pp. 104-110

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In the paper we study a formula of the regularized trace for a perturbation in Schatten–von Neumann class ($\sigma_p$, $p\in\mathbb N$) of discrete self-adjoint operators. We prove that the regularized vanishes after deducting $(p-1)$ terms of perturbation theory if there are no dilating gaps in the spectrum of the unperturbed operator.
Keywords: perturbation theory, regularized trace, discrete operator, spectrum, resolvent. 
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     author = {Kh. Kh. Murtazin and Z. Yu. Fazullin},
     title = {Formula of the regularized trace for perturbation in the {Schatten--von} {Neumann} of discrete operators},
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Kh. Kh. Murtazin; Z. Yu. Fazullin. Formula of the regularized trace for perturbation in the Schatten--von Neumann of discrete operators. Ufa mathematical journal, Tome 7 (2015) no. 4, pp. 104-110. http://geodesic.mathdoc.fr/item/UFA_2015_7_4_a9/