  In this paper we study the convergence of a Lie-Trotter operator splitting
for stochastic semi-linear evolution equations in a Hilbert space. The abstract
Hilbert space setting allows for the consideration of convergence of the
approximation for both the original and spatially discretized problems. It is
known that the strong convergence of this scheme is classically of half-order,
at best. We demonstrate that this is in fact the optimal order of convergence
in the proposed setting, with the actual order being dependent upon the
regularity of noise collected from applications.
