Let f be a function in the Douglas algebra A and let I be a finitely generated ideal in A. We give an estimate for the distance from f to I that allows us to generalize a result obtained by Bourgain for to arbitrary Douglas algebras.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm148-1-3, author = {Pamela Gorkin and Raymond Mortini and Daniel Su\'arez}, title = {An upper bound for the distance to finitely generated ideals in Douglas algebras}, journal = {Studia Mathematica}, volume = {147}, year = {2001}, pages = {23-36}, zbl = {0996.46020}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm148-1-3} }
Pamela Gorkin; Raymond Mortini; Daniel Suárez. An upper bound for the distance to finitely generated ideals in Douglas algebras. Studia Mathematica, Tome 147 (2001) pp. 23-36. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm148-1-3/