Dense Stable Rank and Runge Type Approximation Theorems for H^∞ Maps

2020/06/07 by Alexander Brudnyi, Brudnyi, Alexander
Mathematics · #30H05 #30H50 #Advanced Banach Space Theory #Advanced Topics in Algebra #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2006.04179

openalex publication_date 2020/06/07 · openalex created_date 2020/06/12 · openalex updated_date 2026/07/28

Abstract

Let H^∞(\mathbb D×\N) be the Banach algebra of bounded holomorphic functions defined on the disjoint union of countably many copies of the open unit disk \mathbb D⊂\mathbb C. We show that the dense stable rank of H^∞(\mathbb D×\N) is one and using this fact prove some nonlinear Runge-type approximation theorems for H^∞(\mathbb D×\N) maps. Then we apply these results to obtain a priori uniform estimates of norms of approximating maps in similar approximation problems for algebra H^∞(\mathbb D).

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