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

TL;DR

This paper establishes a maximality theorem for one-parameter dynamical systems, extending to multiplier systems and employing harmonic analysis, topological vector spaces, and operator algebra techniques.

Contribution

It provides a new maximality characterization for one-parameter dynamical systems, including multiplier systems, with novel methods applicable even to commutative multiplier algebras.

Findings

Proves a maximality theorem for one-parameter dynamical systems.

Extends results to multiplier one-parameter dynamical systems.

Introduces new methods combining harmonic analysis and operator algebra techniques.

Abstract

We prove a maximality theorem for one-parameter dynamical systems including multiplier one-parameter dynamical systems. Our main result is new even for one-parameter actions on commutative multiplier algebras including the algebra of bounded continuous functions on the set of real numbers 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.