An abstract formula for regularized traces of discrete operators and its applications

In this paper, we prove an abstract formula for regularized traces of discrete operators in a separable Hilbert space. This formula is a generalization of the formula for the first regularized trace to the case of higher-order traces. We also discuss applications of the formula obtained to a wide class of discrete operators acting in the Bergman space that are generalizations of the Gribov operator from Reggeon field theory.