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

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 $H^{\infty }+C$.

v1: 16 pages

References in corpus (2)

• The Matrix-Valued $H^p$ Corona Problem in the Disk and Polydisk
• The Bass and Topological Stable Ranks of $H^\infty_\R(\D)$ and $A_\R(\D)$

Cited by in corpus (3)

• Fredholmness and compactness of truncated Toeplitz and Hankel operators
• The covering dimension of a distinguished subset of the spectrum $M(H^{\infty })$ of $H^{\infty }$ and the algebra of real-symmetric and continuous functions on $M(H^{\infty })$
• Factorization by elementary matrices, null-homotopy and products of exponentials for invertible matrices over rings