Traces of operators with relatively compact perturbations

V. A. Sadovnichii   ; V. E. Podolskii

Sbornik. Mathematics, Tome 193 (2002) no. 2, pp. 279-302

Résumé

Regularized trace formulae are proved for abstract operators with a perturbing operator $B$ subordinate to the non-perturbed operator $A_0$ in the following sense: $BA_0^{-1}$ is a compact operator in some Schatten–von Neumann class of finite order. Two essentially different cases can be distinguished here: the resolvent of $A_0$ 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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