We prove bounds for a class of unital homomorphisms arising in the study of spectral sets, by involving extremal functions and vectors. These are used to recover three celebrated results on spectral constants by Crouzeix--Palencia, Okubo--Ando and von Neumann in a unified way and to refine a recent result by Crouzeix--Greenbaum.

翻译：我们通过涉及极值函数和向量，证明了在谱集研究中出现的一类单位同态的有界性。这些结果被用于以统一的方式重构Crouzeix–Palencia、Okubo–Ando和von Neumann关于谱常数的三个著名结论，并改进了Crouzeix–Greenbaum的一个最新结果。