In this article, the question of whether the Löwner partial order on the positive cone of an operator algebra is determined by the norm of any arbitrary Kubo–Ando mean is studied. The question was affirmatively answered for certain classes of Kubo–Ando means, yet the general case was left as an open problem. We here give a complete answer to this question, by showing that the norm of every symmetric Kubo–Ando mean is order-determining, i.e., if $A,B\in \mathcal B(H)^{++}$ satisfy $\Vert A\sigma X\Vert \le \Vert B\sigma X\Vert $ for every $X\in \mathcal {A}^{{++}}$, where $\mathcal A$ is the C*-subalgebra generated by $B-A$ and I, then $A\le B$.

本文研究了算子代数正锥上的 Löwner 偏序是否由任意 Kubo-Ando 均值的范数决定的问题。对于某些类别的久保安藤手段，这个问题得到了肯定的回答，但一般情况仍是一个悬而未决的问题。我们在这里给出了这个问题的完整答案，通过证明每个对称 Kubo-Ando 均值的范数是顺序确定的，即，如果$A,B\in \mathcal B(H)^{++}$满足$ \Vert A\sigma X\Vert \le \Vert B\sigma X\Vert $对于每个$X\in \mathcal {A}^{{++}}$，其中$\mathcal A$是 C*-由$BA$和I生成的子代数，然后是$A\le B$。