A uniform algebra approach to an approximation theorem of Sahutoglu and Tikaradze

TL;DR

This paper employs uniform algebra techniques to provide a simplified proof of an approximation theorem, extending the result to open sets where Gleason's problem is solvable, beyond the original $L^$-pseudoconvex domains.

Contribution

It introduces a new proof method using uniform algebras for an existing approximation theorem, broadening its applicability to more general open sets.

Findings

Simplified proof of the approximation theorem

Extension to open sets with solvable Gleason's problem

Broader applicability beyond $L^$-pseudoconvex domains

Abstract

Using methods from the theory of uniform algebras, we give a simple proof of an approximation result of Sahutoglu and Tikaradze with $L^\infty$-pseudoconvex domains replaced by the open sets for which Gleason's problem is solvable.