Let X be a completely regular Hausdorff space and \(C_b(X)\) be the space of all bounded continuous functions on X, equipped with the strict topology \(\beta \). We study some important classes of \((\beta ,\Vert \cdot \Vert _E)\)-continuous linear operators from \(C_b(X)\) to a Banach space \((E,\Vert \cdot \Vert _E)\): \(\beta \)-absolutely summing operators, compact operators and \(\beta \)-nuclear operators. We characterize compact operators and \(\beta \)-nuclear operators in terms of their representing measures. It is shown that dominated operators and \(\beta \)-absolutely summing operators \(T:C_b(X)\rightarrow E\) coincide and if, in particular, E has the Radon–Nikodym property, then \(\beta \)-absolutely summing operators and \(\beta \)-nuclear operators coincide. We generalize the classical theorems of Pietsch, Tong and Uhl concerning the relationships between absolutely summing, dominated, nuclear and compact operators on the Banach space C(X), where X is a compact Hausdorff space.

设X是完全正豪斯多夫空间和\（C_B（X）\）是对所有有界连续函数的空间X，配备了严格的拓扑结构\（\测试\） 。我们研究了\（（\ beta，\ Vert \ cdot \ Vert _E）\）的一些重要类-从\（C_b（X）\）到Banach空间\（（E，\ Vert \ cdot \ Vert _E）\）：\（\ beta \）-绝对求和运算符，紧凑型运算符和\（\ beta \）-核运算符。我们根据其表示度量来表征紧凑算子和\（\ beta \）核算子。结果表明，主导运营商和\（\ beta \）-绝对求和运算符\（T：C_b（X）\ rightarrow E \）重合，并且特别是如果E具有Radon–Nikodym属性，则\（\ beta \）-绝对求和运算符和\（\ beta \）-核运算符重合。我们推广了Pietsch，Tong和Uhl的经典定理，涉及Banach空间C（X）上绝对求和，支配，核和紧凑算子之间的关系，其中X是紧凑的Hausdorff空间。