We introduce and study a scale of operator classes on the annulus that is motivated by the $\mathcal{C}_{\rho}$ classes of $\rho$-contractions of Nagy and Foia\c{s}. In particular, our classes are defined in terms of the contractivity of the double-layer potential integral operator over the annulus. We prove that if, in addition, complete contractivity is assumed, then one obtains a complete characterization involving certain variants of the $\mathcal{C}_{\rho}$ classes. Recent work of Crouzeix-Greenbaum and Schwenninger-de Vries allows us to also obtain relevant K-spectral estimates, generalizing existing results from the literature on the annulus. Finally, we exhibit a special case where these estimates can be significantly strengthened.

翻译：本文引入并研究了一类在环形区域上定义的算子类尺度，其动机源于Nagy和Foaş关于ρ-压缩算子的$\mathcal{C}_{\rho}$类。具体而言，我们的算子类通过环形区域上双层位势积分算子的压缩性来定义。我们证明，若进一步假设完全压缩性，则可获得涉及$\mathcal{C}_{\rho}$类某些变体的完整刻画。Crouzeix-Greenbaum与Schwenninger-de Vries的近期工作使我们能够进一步推导相关的K-谱估计，从而推广了环形区域上的现有文献结果。最后，我们展示了一个特例，其中这些估计可被显著加强。