Nondegenerate actions on Hilbert C*-modules

Let X be a (right) Hilbert C*-module and let B be a C*-algebra acting on X from the left via adjointable operators. In this note we establish the equivalence of two notions of nondegeneracy for such an action of B on X. Furthermore, we explain how techniques from an earlier paper of Kim can be used to give a short proof of a recent result of Dessi, Kakariadis and Paraskevas.