In this paper, we investigate maps on sets of positive operators which are induced by the continuous functional calculus and transform a Kubo–Ando mean \(\sigma \) into another \(\tau \). We establish that under quite mild conditions, a mapping \(\phi \) can have this property only in the trivial case, i.e. when \(\sigma \) and \(\tau \) are nontrivial weighted harmonic means and \(\phi \) stems from a function which is a constant multiple of the generating function of such a mean. In the setting where exactly one of \(\sigma \) and \(\tau \) is a weighted arithmetic mean, we show that under fairly weak assumptions, the mentioned transformer property never holds. Finally, when both of \(\sigma \) and \(\tau \) are such a mean, it turns out that the latter property is only satisfied in the trivial case, i.e. for maps induced by affine functions.

在本文中，我们研究了由连续函数演算引起的正算子集上的映射，并将Kubo-Ando均值\（\ sigma \）转换为另一个\（\ tau \）。我们确定，在相当温和的条件下，映射\（\ phi \）仅在平凡的情况下才具有此属性，即，当\（\ sigma \）和\（\ tau \）是非平凡的加权调和均值和\（\ phi \）源于一个函数，该函数是此类平均值的生成函数的常数倍。在\（\ sigma \）和\（\ tau \）之一的位置是一个加权算术平均值，我们表明在相当弱的假设下，所提到的变压器性质永远不会成立。最终，当\（\ sigma \）和\（\ tau \）都是这样的平均值时，事实证明，后者的属性仅在平凡的情况下才满足，即对于仿射函数引起的映射。