Topological Radicals of Semicrossed Products

TL;DR

This paper characterizes the hypocompact radical of semicrossed products using properties of the underlying dynamical system, linking algebraic elements to dynamical features like recurrent points.

Contribution

It provides a new characterization of the hypocompact radical in semicrossed products based on Fourier coefficients and dynamical system properties.

Findings

Hypocompact radical elements vanish on recurrent points.

Fourier coefficients vanish on the largest perfect subset of X.

Characterization connects algebraic radicals with dynamical system topology.

Abstract

We characterize the hypocompact radical of a semicrossed product in terms of properties of the dynamical system. We show that an element A of a semicrossed product is in the hypocompact radical if and only if the Fourier coefficients of A vanish on the closure of the recurrent points and the 0-Fourier coefficient vanishes also on the largest perfect subset of X.