CONE STRUCTURE OF L<sup>2</sup>-WASSERSTEIN SPACES
CONE STRUCTURE OF L<sup>2</sup>-WASSERSTEIN SPACES
The aim of this paper is to obtain a better understanding of the geometric structure of quadratic Wasserstein spaces over separable Hilbert spaces. For this sake, we focus on their cone and product structures, and prove that the quadratic Wasserstein space over any separable Hilbert space has a cone structure …