$$L_p-$$Bounds for the Krein Spectral Shift Function: $$0<p<\infty$$

Abstract

We extend the inequalities originally obtained by D. Hundertmark and B. Simon for $$L_p-$$ bounds, $$1\leq p\leq \infty$$ , for the Krein spectral shift function to the setting of general semifinite von Neumann algebras. We also complete these results by showing that in the quasi-normed setting, for example, for $$L^p$$ -spaces with $$0<p\le 1$$ , a converse inequality holds.