Abstract harmonic analysis on locally compact right topological groups

TL;DR

This paper extends the theory of Haar measures and analytic properties to locally compact right topological groups, providing new conditions for their existence and generalizing classical results beyond the compact admissible case.

Contribution

It introduces sufficient conditions for Haar measure existence on locally compact right topological groups and generalizes analytic theory to this broader setting.

Findings

Established new criteria for Haar measure existence

Generalized analytic properties to non-compact right topological groups

Characterized Haar measure existence without admissibility constraints

Abstract

Analytic properties of right topological groups have been extensively studied in the compact admissible case (i.e when the group has a dense topological center). This was inspired by the existence of a Haar measure on such groups. In this paper, we broaden the scope of this work. We give (similar) sufficient conditions for the existence of a Haar measure on locally compact right topological groups and generalize analytic theory to this setting. We then define new measure algebra analogues in the compact setting and use these to completely characterize the existence of a Haar measure, producing sufficient conditions that do not rely on admissibility.