On singular value inequalities for matrix means

Abstract

For positive semidefinite $n\times n$ matrices $A$ and $B$, the singular value inequality $(2+t)s_j(A^r{B}^{2-r}+A^{2-r}{B}^r)\le 2s_j(A^2+tAB+B^2)$ is shown to hold for $r=\frac{1}{2},1,\frac{3}{2}$ and all $-2<t\le 2$.

8 pages