Two areas of mathematics which have received substantial attention in recent years are the theory of optimal transport and the Elliott classification programme for ${\mathrm{C}}^{⁎}$-algebras. We combine these two seemingly unrelated disciplines to make progress on a classical problem of Weyl. In particular, we show how results from the Elliott classification programme can be used to translate continuous transport of spectral measures into optimal unitary conjugation in ${\mathrm{C}}^{⁎}$-algebras. As a consequence, whenever two normal elements of a sufficiently well-behaved ${\mathrm{C}}^{⁎}$-algebra share a spectrum amenable to such continuous transport, and have trivial $K_1$-class, the distance between their unitary orbits can be computed tracially.

近年来，数学受到了极大关注的两个领域是最优运输理论和Elliott分类程序。 ${\mathrm{C}}^{⁎}$-代数。我们将这两个看似无关的学科结合起来，在经典的韦尔问题上取得了进步。特别是，我们展示了如何使用Elliott分类程序的结果将光谱测量的连续传输转化为最佳的单共轭。${\mathrm{C}}^{⁎}$-代数。结果，只要两个正常元素的行为充分${\mathrm{C}}^{⁎}$-代数共享适用于这种连续传输的频谱，并且微不足道 ${ķ}_{\mathrm{1个}}$-class，它们的单位轨道之间的距离可以通过种族计算。