For a Hilbert space $H$ the Riesz representation theorem states that $H$ is isomorphic to its dual $H^*$ via $x \mapsto \langle x, -\rangle$.

It is often stated in the litterature that this does not work in full generality for an Hilbert module over a $C^*$ algebra. For exemple when one want to define the adjoint of a morphism between hilbert modules, one can be stucked by the non existence of such a representation theorem. At the end (the end of the beggining), we define a morphism of hilbert module to be a function that admit an adjoint.

Is there a simple counterexample to Ries representability for hilbert module ?