Diffusion Processes on $p$-Wasserstein Space over Banach Space

To study diffusion processes on the p-Wasserstein space $\mathscr P_p$ for $p\in [1,\infty)$ over a separable, reflexive Banach space $X$, we present a criterion on the quasi-regularity of Dirichlet forms in $L^2(\mathscr P_p,Λ)$ for a reference probability $Λ$ on $\mathscr P_p$. It is formulated in