Von Neumann type trace inequalities for Schatten-class operators

We generalize von Neumann's well-known trace inequality, as well as related eigenvalue inequalities for Hermitian matrices, to Schatten-class operators between complex Hilbert spaces of infinite dimension. To this end, we exploit some recent results on the C-numerical range of Schatten-class operators . For the readers' convenience, we sketched the proof of these results in the Appendix.