Weak uniqueness for stochastic partial differential equations in Hilbert spaces

Let U, H be two separable Hilbert spaces. The main goal of this paper is to study weak uniqueness of a Stochastic Differential Equation evolving in H of the form (Formula presented.) where {W(t)}t≥0 is a U-cylindrical Wiener process, A:D(A)⊆H→H is the infinitesimal generator of a strongly continuous semigroup, V,G:U→H are linear bounded operators and B:H→U is a locally uniformly continuous function. The abstract result in the paper gives weak uniqueness for a large class of heat and damped equations in any dimension without any Hölder continuity assumption on B.