In earlier work a crossed product of a Banach algebra was constructed from a Banach
algebra dynamical system $(A, G,\alpha) $ and a class $\mathcal {R} $ of continuous
covariant representations, and its representations were determined. In this paper the theory
is developed further. We consider the dependence of the crossed product on the class
$\mathcal {R} $ and its essential uniqueness. Next we study generalized Beurling algebras:
weighted Bochner spaces of $ A $-valued functions on $ G $ with a continuous …

We construct a crossed product Banach algebra from a Banach algebra dynamical system
$(A, G,\alpha) $ and a given uniformly bounded class $ R $ of continuous covariant Banach
space representations of that system. If $ A $ has a bounded left approximate identity, and $
R $ consists of non-degenerate continuous covariant representations only, then the non-
degenerate bounded representations of the crossed product are in bijection with the non-
degenerate $ R $-continuous covariant representations of the system. This bijection, which …