2010/12/21 by Artur Nicolau, Nicolau, Artur, Daniel Suárez +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1012.4644
openalex publication_date 2010/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterize the connected components of the subset \cni of H^∞ formed by the products bh, where b is Carleson-Newman Blaschke product and h∈ H^∞ is an invertible function. We use this result to show that, except for finite Blaschke products, no inner function in the little Bloch space is in the closure of one of these components. Our main result says that every inner function can be connected with an element of \cni within the set of products uh, where u is inner and h is invertible. We also study some of these issues in the context of Douglas algebras.