Stable Ranks for the Sarason

Abstract

We prove a Corona type theorem with bounds for the Sarason algebra H∞ + C and determine its spectral characteristics, thus continuing a line of research initiated by N. Nikolski. We also determine the Bass, the dense, and the topological stable ranks of H∞ + C. To fix our setting, let A be a commutative unital Banach algebra with unit e and M(A) its maximal ideal space. The following concept of spectral characteristics was introduced by N. Nikolski [15]. For a ∈ A, let â denote the Gelfand transform of a. We let

Cite this paper

@inproceedings{Wick2009StableRF, title={Stable Ranks for the Sarason}, author={Brett D. Wick}, year={2009} }