Spectrum of bidual uniform algebras
Marek Kosiek, Krzysztof Rudol

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 of a uniform algebra . This spectrum turns out to be a quotient space of the hyper-Stonean envelope of the spectrum of .
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Holomorphic and Operator Theory
