Banach Intermediate Spaces for Gaussian Fr\'{e}chet Spaces

Abstract

In this article, we show that every centered Gaussian measure on an infinite dimensional separable Fr\'{e}chet space $X$ over $\mathbb R$ admits some full measure Banach intermediate space between $X$ and its Cameron-Martin space. We provide a way of generating such spaces and, by showing a partial converse, give a characterization of Banach intermediate spaces. Finally, we show an example of constructing an $\alpha$-H\"older intermediate space in the space of continuous functions, $\mathcal C_0[0, 1]$ with the classical Wiener measure.