A characterization of the disk algebra


Cole B., Sadik N., Poletsky E.

ILLINOIS JOURNAL OF MATHEMATICS, vol.46, no.2, pp.533-539, 2002 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 2
  • Publication Date: 2002
  • Journal Name: ILLINOIS JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.533-539
  • Istanbul University Affiliated: No

Abstract

We prove that a complex unital uniform algebra is isomorphic to the disk algebra if and only if every closed subalgebra with one generator is isomorphic to the whole algebra. Moreover, every such subalgebra of the disk algebra is isometrically isomorphic to the disk algebra. On the way we prove: (1) for a function f in the disk algebra the interior of the polynomial hull of the set f ((U) over bar), where (U) over bar is the closed unit disk, is a Jordan domain; (2) if a uniform algebra A on a compact Hausdorff set X containing the Cantor set separates points of X, then there is f is an element of A such that f(X) = (U) over bar.