Rank-one operators in reflexive one-sided<Emphasis Type="Italic">A</Emphasis>-submodules

In this paper, we first characterize reflexive one-sided A-submodulesU of a unital operator algebraA inB(H) completely. Furthermore we investigate the invariant subspace lattice LatR and the reflexive hull RefR, whereR is the submodule generated by rank-one operators inU; in particular, ifL is a subspace lattice, we obtain when the rank-one algebraR of AlgL is big enough to determined AlgL in the following senses: AlgL = Alg LatR and AlgL = RefR.