Banach Intermediate Spaces for Gaussian Fréchet Spaces

Abstract

In this article, we show that every centered Gaussian measure on an infinite dimensional separable Fréchet 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 $\alpha$-Hölder intermediate space in the space of continuous functions, ${\mathcal{C}}_0[0,1]$ with the classical Wiener measure.

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