Stereotype approximation property for the group algebra ${\mathcal C}^\star(G)$ of measures

TL;DR

This paper proves that the group algebra of measures on any locally compact group always possesses the stereotype approximation property, a stronger form of the classical approximation property.

Contribution

It establishes that the group algebra of measures on any locally compact group has the stereotype approximation property, advancing understanding of approximation properties in harmonic analysis.

Findings

Group algebra of measures on any locally compact group has the stereotype approximation property.

The stereotype approximation property is a stronger condition than the classical approximation property.

The result applies universally to all locally compact groups.

Abstract

The stereotype approximation property is formally a stronger condition than the classical approximation property, and because of that the question which spaces possess the stereotype approximation property is quite difficult. In this paper we show that the group algebra ${\mathcal C}^\star(G)$ of measures on a locally compact grop $G$ always has this property.