A trace class operator inequality
The author extends the trace inequality \(\text{tr}[(AB)^n]\leq(\text{tr\,}A)^n (\text{tr\,}B)^n\), \(\forall n\in\mathbb{N}\), known for positive semidefinite matrices, to positive trace class Hilbert space operators \(A,B\). The proof is based on simultaneous approximation of \(A\) and \(B\) by finite-dimensional operators.
scientific article; zbMATH DE number 5124046