The corona theorem for matrices
type: Item
instance of: scholarly article
title: The corona theorem for matrices
zbMATH Open document ID: 0648.30039
DOI: 10.1007/BF01161999
author: Mats Andersson
published in: Mathematische Zeitschrift
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174039
review text: Let F be an \(r\times k\)-matrix of bounded holomorphic functions in the unit disc such that the nonzero eigenvalues of \(FF^ *\) are bounded from below by some \(\delta >0\). We prove that there is a bounded holomorphic solution to \(Fu=g\) if g is an r-column of bounded holomorphic functions and the equation is solvable pointwise. If \(r=1\), this is Carleson's corona theorem.
Mathematics Subject Classification ID: 30H05
zbMATH DE Number: 4057902
zbMATH Keywords: corona theorem
MaRDI profile type: Publication
cites work: Wolff's proof of the corona theorem
cites work: Q3922907
cites work: Generators for some rings of analytic functions
cites work: Morphismes surjectifs de fibrés vectoriels semi-positifs
description: scientific article; zbMATH DE number 4057902