arXiv: Functional Analysis | 2019
Von Neumann Type of Trace Inequalities for Schatten-Class Operators
Abstract
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.