English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this note we prove that the Bass stable rank of $H^\infty_\R(\D)$ is two.This establishes the validity of a conjecture by S. Treil. We accomplish thisin two different ways, one by giving a direct proof, and the other, by firstshowing that the topological stable rank of $H^\infty_\R(\D)$ is two. We applythese results to give new proofs of results by R. Rupp and A. Sasane statingthat the Bass stable rank of $A_\R(\D)$ is two and the topological stable rankof $A_\R(\D)$ is two, settling a conjecture by the second author. We alsopresent a $\bar\partial$-free proof of the second author's characterization ofthe reducible pairs in $A_\R(\D)$.

The Bass and Topological Stable Ranks of $H^\infty_\R(\D)$ and $A_\R(\D)$