Extensions of interpolation between the arithmetic-geometric mean inequality for matrices

摘要

In this paper, we present some extensions of interpolation between the arithmetic-geometric means inequality. Among other inequalities, it is shown that if A, B, X are n × n $nimes n$ matrices, then ∥ A X B ∗ ∥ 2 ≤ ∥ f 1 ( A ∗ A ) X g 1 ( B ∗ B ) ∥ ∥ f 2 ( A ∗ A ) X g 2 ( B ∗ B ) ∥ , $$egin{aligned} iglVert AXB^{*} igrVert ^{2}leq iglVert f_{1} igl(A^{*}Aigr)Xg_{1}igl(B^{*}Bigr) igrVert iglVert f_{2}igl(A^{*}Aigr)Xg_{2}igl(B^{*}Bigr) igrVert , end{aligned}$$ where f 1 $f_{1}$ , f 2 $f_{2}$ , g 1 $g_{1}$ , g 2