Factorization of positive definite kernels. Correspondences: $C^{\ast }$-algebraic and operator valued context vs scalar valued kernels

Palle E. T. Jorgensen, James Tian

We introduce and study a class $\mathcal{M}$ of generalized positive definite kernels of the form $K:X\times X\to L(\mathfrak{A},L(H))$, where $\mathfrak{A}$ is a unital $C^{…