Closability of Module σ−Derivatoins

Let σ be a linear mapping from a dense subalgebra A of a Banach algebra B into B. In this note, we study the closability of a module σ− derivation δ from A into a B− bimodule M. Applying the notions of torsion-free modules and essential ideals, we present several results concerning the closability of such derivations. Also we investigate the closability of module σ− derivations of the C ∗− algebra B into a Hilbert B− bimodule M