Suppose that X is the subspace of the set of probability measures on the classical Wiener space $C[0,T]$, for some $T>0$, comprised of Gaussian measures. 


In the finite-dimensional setting, the Wasserstein metric between two Gaussian random-variables has a very convenient form.... Are there any known analogues for the infinite dimensional setting? Especially, in the case of the classical Wiener space?



Reference Request: 2-Wasserstein Metric on Wiener Space
This is discussed thoroughly in the following reference; see Section 3 and specifically Theorem 3.5.


*Gelbrich, Matthias*, [**On a formula for the $L^2$ Wasserstein metric between measures on Euclidean and Hilbert spaces**](http://dx.doi.org/10.1002/mana.19901470121), Math. Nachr. 147, 185-203 (1990). [ZBL0711.60003](https://zbmath.org/?q=an:0711.60003).


