Operator-valued positive definite kernels and differentiable universality

We present a characterization for positive definite operator-valued kernel to be universal or [Formula: see text]-universal, and apply these characterizations family of kernels that are shown well behaved. Later, we obtain an differentiable text]-universal text]-universal. In order such examples, generalize some well-known results concerning the structure context. On examples is given emphasis on radial Euclidean spaces.