Grand Lebesgue Spaces are really Banach algebras relative to the convolution on unimodular locally compact groups

TL;DR

This paper proves that Grand Lebesgue Spaces on unimodular locally compact groups form Banach algebras under convolution, extending their algebraic structure in harmonic analysis.

Contribution

It establishes that Grand Lebesgue Spaces are Banach algebras with respect to convolution on unimodular locally compact groups, a novel structural insight.

Findings

Grand Lebesgue Spaces form Banach algebras under convolution

Extension of algebraic properties to new function spaces

Applicable to harmonic analysis on groups

Abstract

We prove that the Grand Lebesgue Space, builded on a unimodular locally compact topological group, forms a Banach algebra relative to the convolution.