Unimodular approximation in function algebras

John McDonald

Vol. 122 (1986), No. 2, 435–440

DOI: 10.2140/pjm.1986.122.435

Abstract

Let A be a function algebra on the compact Hausdorff space X. The main result of this paper gives necessary and sufficient conditions for the set of quotients of inner functions in A to be dense in the set of continuous unimodular functions on X. A theorem of Douglas and Rudin concerning quotients of Blaschke products is derived. The main result is also applied in the context of the theory of compact abelian groups.

Mathematical Subject Classification 2000

Primary: 46J15

Secondary: 41A65, 46J10

Milestones

Received: 10 September 1984

Revised: 20 March 1985

Published: 1 April 1986