Radonification Problem for Cylindrical Measures on Tensor Products of Banach Spaces

Abstract

An operator _w_1⊗_w_2 is said to be p-Radonifying if it maps every cylindrical measure of type p, defined on the tensor product E_⊗_F of two Banach spaces, into a Radon probability cf order p on the completion of some normed product G_⊗_αH. In this paper we prove that α is p-Radonifying, 1<p<∞ if and only if it is _p_∼-summing.