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# Journal of Operator Theory

Volume 84, Issue 2, Fall 2020  pp. 323-338.

Von Neumann type trace inequalities for Schatten-class operators

Authors:  Gunther Dirr (1), Frederik vom Ende (2)
Author institution: (1) Institute of Mathematics, University of Wurzburg, D-97074 Wurzburg, Germany
(2) Department of Chemistry, Technische Universitaet Munchen, D-85747 Garching, Germany and Munich Centre for Quantum Science and Technology (MCQST), D-80799~Munchen, Germany

Summary: 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.

DOI: http://dx.doi.org/10.7900/jot.2019jun03.2241
Keywords: $C$-numerical range, Schatten-class operators, von Neumann inequality, trace inequality