Article

    Ufa Mathematical Journal
    Volume 7, Number 4, pp. 104-110

    Regularized trace formula for discrete operators with a perturbation in the Schatten-von Neumann class


    Fazullin Z.Yu., Murtazin Kh.Kh.

    DOI:10.13108/2015-7-4-104

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    In the paper we study a regularized trace formula for discrete self-adjoint operators with a perturbation in Schatten-von Neumann class ($\sigma_{p},p\in\mathds{N}$). We prove that the regularized trace vanishes after deducting $(p-1)$ terms of perturbation theory if there are no dilating gaps in the spectrum of the unperturbed operator.