Spectral Characteristics and Stable Ranks for the Sarason Algebra $H^\infty+C$

TL;DR

This paper investigates the spectral properties and stable ranks of the Sarason algebra $H^ Infty+C$, providing a Corona theorem with bounds and detailed rank computations.

Contribution

It establishes a Corona theorem with bounds for $H^ Infty+C$ and determines its spectral characteristics and stable ranks, advancing understanding of this algebra.

Findings

Proved a Corona type theorem with bounds for $H^ Infty+C$

Determined the spectral characteristics of $H^ Infty+C$

Calculated the Bass, dense, and topological stable ranks of $H^ Infty+C$

Abstract

We prove a Corona type theorem with bounds for the Sarason algebra $H^\infty+C$ and determine its spectral characteristics. We also determine the Bass, the dense, and the topological stable ranks of $H^\infty+C$.