Abstract
Regularized trace formulae are proved for abstract operators with a perturbing operator subordinate to the non-perturbed operator in the following sense: is a compact operator in some Schatten-von Neumann class of finite order. Two essentially different cases can be distinguished here: the resolvent of is either of trace class or not. Five theorems describing various cases of operator subordination and the structure of the spectrum of the unperturbed operator are proved.
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