Extension problems and stable rank in commutative Banach algebras
The concept of stable rank was introduced by H. Bass. In recent papers of G. Corach (with the collaboration of F. D. Suarez and A. R. Larotonda) stable rank conditions on a Banach algebra are related to the topology of its spectrum. In these two papers the authors applied previous results and algebraic- topological properties to estimate the stable rank of commutative Banach algebras; in particular, holomorphic function algebras. For example, in the first paper they show that the topological stable rank of \(A(\Delta^ n)\) is \(n+1\) while in the second they show that the (Bass) stable rank of this algebra lies between \([n/2]+1\) and n. Several open problems are stated, in particular, to calculate the exact value of the topological stable rank of \(A(\Delta^ n)\) for \(n\geq 3\).
calculate the exact value of the topological stable rank
scientific article; zbMATH DE number 3979783
scientific article