Eigenvalues of majorized Hermitian matrices and Littlewood–Richardson coefficients Original Research Article

Answering a question raised by S. Friedland, we show that the possible eigenvalues of Hermitian matrices (or compact operators) A, B, and C with Cless-than-or-equals, slantA+B are given by the same inequalities as in Klyachkoʹs theorem for the case where C=A+B, except that the equality corresponding to tr(C)=tr(A)+tr(B) is replaced by the inequality corresponding to tr(C)less-than-or-equals, slanttr(A)+tr(B). The possible types of finitely generated torsion modules A, B, and C over a discrete valuation ring such that there is an exact sequence B→C→A are characterized by the same inequalities.