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：我们通过利用极端功能和矢量来证明光谱组研究中产生的一类单位同质体的界限,这些功能和矢量用来以统一的方式回收Crouzix-Palencia、Okubo-Ando和von Neumann在光谱常数上的三种值得庆祝的结果,并改进Crouzix-Greenbaum最近的结果。