  Using representation theory techniques we prove that various spaces of
derivations or one-sided multipliers over certain operator algebras are
reflexive. A sample result: any bounded local derivation (local left
multiplier) on an automorphic semicrossed product is a derivation (resp. left
multiplier). In the process we obtain various results of independent interest.
In particular, the finite dimensional nest representations of the tensor
algebra of a topological graph separate points.
