Radonification Problem for Cylindrical Measures on Tensor Products of Banach Spaces

Abstract

An operator $w_1\otimes w_2$ is said to be $p$-Radonifying if it maps every cylindrical measure of type $p$, defined on the tensor product $E\otimes F$ of two Banach spaces, into a Radon probability cf order $p$ on the completion of some normed product $G{\otimes }_{\alpha }H$. In this paper we prove that $w_1\otimes w_2$ is $p$-Radonifying, $1<p<\infty$ if and only if it is $\tilde{p}$-summing.