Radonifying operators and infinitely divisible Wiener integrals

In this article we illustrate the relation between the existence of Wiener integrals with respect to a Lévy process in a separable Banach space and radonifying operators. For this purpose, we introduce the class of $\vartheta$-radonifying operators, i.e. operators which map a cylindrical measure $\vartheta$ to a genuine Radon measure. We study this class of operators for various examples of infinitely divisible cylindrical measures $\vartheta$ and highlight the differences from the Gaussian case.