Abstract
A trace formula is obtained for unbounded discrete operators perturbed by a Hilbert-Schmidt operator; this formula may be called the discrete analogue of M. Krein's formula for nuclear perturbations. A regularized trace formula of Krein's type is also proved for perturbations in the class , , for arbitrary compact and relatively compact perturbations depending on the behaviour at infinity of the distribution function of the spectrum of the unperturbed operator.
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