In this paper, we investigate conditionally completely positive definite kernels in the setting of Hilbert \(C^*\)-modules. At first, we present a correspondence between conditionally completely positive definite kernels and completely positive definite kernels. Utilizing this relation, we give the Kolmogorov decomposition for a certain conditionally completely positive definite kernel. We present a characterization of conditionally completely positive definite kernels majorized by a kernel under some mild conditions. Finally, as an application of this decomposition, we find a sufficient condition for the existence of an extreme point of a convex set consisting of some special kernels.

在本文中，我们研究了Hilbert \（C ^ * \）- modules设置中的条件完全正定核。首先，我们提出条件完全正定核与完全正定核之间的对应关系。利用这种关系，我们给出了某个条件完全正定核的Kolmogorov分解。我们提出了在某些温和条件下由一个核主化的条件完全正定核的特征。最后，作为这种分解的一种应用，我们找到了由某些特殊核组成的凸集的极点存在的充分条件。