2012/12/03 by Ronald G. Douglas, Douglas, Ronald G.
Mathematics · #30H80 #32A35 #32A36 #32A38 #32A65 #32A70 #46A15 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.CV #math.FA #msc:30H80 #msc:32A35 #msc:32A36 #msc:32A38 #msc:32A65 #msc:32A70 #msc:46A15
paper · pdf · doi:10.48550/arxiv.1212.0455
arxiv created 2012/12/03 · openalex publication_date 2012/12/03 · arxiv updated 2012/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The corona problem was motivated by the question of the density of the open unit disk D in the maximal ideal space of the algebra, H1(D), of bounded holomorphic functions on D. In this note we study relationships of the problem with questions in operator theory and complex geometry. We use the framework of Hilbert modules focusing on reproducing kernel Hilbert spaces of holomorphic functions on a domain, in Cm. We interpret several of the approaches to the corona problem from this point of view. A few new observations are made along the way. 2012 MSC: 46515, 32A36, 32A70, 30H80, 30H10, 32A65, 32A35, 32A38 Keywords: corona problem, Hilbert modules, reproducing kernel Hilbert space, commutant lifting theorem 1