A solution of the maximality problem for one-parameter dynamical systems

We prove a maximality theorem for one-parameter dynamical systems that include W*-, C*- and multiplier one-parameter dynamical systems. Our main result is new even for one parameter actions on commutative multiplier algebras including the algebra C-b(R) of bounded continuous functions on R acted upon by translations. The methods we develop and use in our characterization of maximality include harmonic analysis, topological vector spaces and operator algebra techniques. (C) 2018 Elsevier Inc. All rights reserved.