Inequalities for mixed Schur functions
Let \(A^ k=(a^ k_{ij})\) be a set of n positive semidefinite matrices each of order n. Let \(\alpha\) : \(S_ n\to {\mathbb{C}}\) where \(S_ n\) is the symmetric group of degree n. The ''mixed Schur function'' is the function of \(A^ 1,...,A^ n\) given by \(\sum \alpha (\sigma) \overline{\alpha (\tau)}\prod^{n}_{i=1}a^ i_{\sigma (i)\tau (i)}\) where \(\sigma\) and \(\tau\) run independently over \(S_ n\). The author obtains an inequality for this function and explores some of the consequences of this inequality.
scientific article; zbMATH DE number 3970947