关于Heinz不等式的注记

NOTES ON AN INEQUALITY OF HEINZ

证明了Ｈｅｉｎｚ不等式ＡＢα≥ＡαＢα（０＜α＜１）对于规范矩阵也成立，还给出了Ｌｏｗｎｅｒ不等式Ａ≥Ｂ≥０时Ａα＞Ｂα的一个初等证明。

Let 0 < α≤1,it is shown that an inequality of Heinz ABα≥AαBαholds fornormal matrices and spectral norm . An elementary proof to the well-known Lowner inequalityA￣α≥ B￣αwith A ≥B≥0 is given.