Opuscula Math. 28, no. 1 (2008), 5-17
Exponential type vectors in Wiener algebras on a Banach ball
Abstract. 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.
Keywords: unitary one-parametric group, Wiener type algebras.
Mathematics Subject Classification: 46E50, 46G25.