Spectrum of bidual uniform algebras

TL;DR

This paper characterizes the spectrum of the bidual of a uniform algebra, showing it as a quotient of the hyper-Stonean envelope of the original spectrum, thus deepening understanding of algebraic duality.

Contribution

It provides a novel description of the spectrum of the bidual algebra as a quotient space of the hyper-Stonean envelope, linking duality and spectral theory.

Findings

Spectrum of $A^{**}$ is a quotient of the hyper-Stonean envelope of $A$'s spectrum.

Establishes a new connection between bidual algebras and hyper-Stonean spaces.

Advances the structural understanding of uniform algebras and their duals.

Abstract

We obtain a description of the spectrum of bidual algebra $A^{**}$ of a uniform algebra $A$. This spectrum turns out to be a quotient space of the hyper-Stonean envelope of the spectrum of $A$.