Exponential type vectors in Wiener algebras on a Banach ball

We consider Wiener type algebras on an open Banach ball. In particular, we prove that such algebras consist of functions analytic in this ball. We also consider a property of one-parameter groups generated by an isometric group acting on a Banach ball. We establish that the subspace of exponential type vectors of its generators form a dense subalgebra in a Wiener algebra and a generator is a derivation on this subspace.