\(H^{\infty}+BUC\) does not have the best approximation property
type: Item
instance of: scholarly article
title: \(H^{\infty}+BUC\) does not have the best approximation property
zbMATH Open document ID: 0584.46044
DOI: 10.1007/BF02384384
published in: Arkiv för Matematik
publication date: 1984-01-01T00:00:00Z
review text: Any closed algebra between \(H^{\infty}\) and \(L^{\infty}\) is called a Douglas algebra. The question had been raised of whether all Douglas algebras had the best approximation property. That is, given any Douglas algebra \({\mathcal D}\) and \(f\in L^{\infty}\) does there exist a \(g\in {\mathcal D}\) such that \(\| f-g\|_{\infty}=\inf \{\| f- g\|_{\infty}:g\in {\mathcal D}\}\). An example is given of such an algebra that does not have this property.
Mathematics Subject Classification ID: 46J30
Mathematics Subject Classification ID: 46J15
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 3935761
zbMATH Keywords: Hardy space
zbMATH Keywords: Douglas algebra
zbMATH Keywords: best approximation property
author: Carl Sundberg
reviewed by: Guillermo López Lagomasino
MaRDI profile type: Publication
cites work: Approximation by compact operators and the space \(H^\infty +C\)
cites work: An Interpolation Problem for Bounded Analytic Functions
cites work: A characterization of Douglas subalgebras
cites work: Q3922907
cites work: Maximal Subalgebras of C(\mathbbΓ)
cites work: The Compact Hankel Operators Form an M-Ideal in the Space of Hankel Operators
cites work: Subalgebras of \(L^\infty\) containing \(H^\infty\)
cites work: Functions of Vanishing Mean Oscillation
cites work: A constructive proof of the Chang-Marshall theorem
cites work: Best Approximation in Certain Douglas Algebras
Recommended article: A counterexample in \(H^{\infty}+BUC\)
Recommended article: Best Approximations in L 1 are Near Best in L p , p < 1
Recommended article: On the Approximation Properties for the SpaceH∞
Recommended article: Q3331728
Recommended article: A counterexample for $H^{\infty}$ approximable functions
Recommended article: Q4311681
Recommended article: Q3507999
Recommended article: Q4452830
Recommended article: The Compact Approximation Property does not imply the Approximation Property
Recommended article: Q3824822
description: scientific article; zbMATH DE number 3935761