A separation property for magnetic Schrödinger operators on Riemannian manifolds

We consider a Schrödinger differential expression L=ΔA+qL=ΔA+q on a complete Riemannian manifold (M,g)(M,g) with metric gg, where ΔAΔA is the magnetic Laplacian on MM and q≥0q≥0 is a locally square integrable function on MM. In the terminology of W.N. Everitt and M. Giertz, the differential expression LL is said to be separated in L2(M)L2(M) if for all u∈L2(M)u∈L2(M) such that Lu∈L2(M)Lu∈L2(M), we have qu∈L2(M)qu∈L2(M). We give sufficient conditions for LL to be separated in L2(M)L2(M).