On the trace formula of perturbation theory. II

In a previous paper for a class of pairs of operators in a Hilbert space wi th nuclear difference or under a more general nuclearity condition there wa s introduced a spectral shift functional. Here we consider the local integr ability of this spectral shift functional, i, e., the problem when this fun ctional can locally be represented by an integrable function. The general r esults are then applied to pairs of definitizable and locally definitizable unitary operators in a Krein space.