An approximation theorem for subalgebras of H_∞

Arne Stray

Vol. 35 (1970), No. 2, 511–515

DOI: 10.2140/pjm.1970.35.511

Abstract

Let E be a closed subset of the unitcircle T = {z : |z| = 1} and denote by B_E the algebra of all functions which are bounded and continuous on the set X = {z : |z|≦ 1&z∉E} and analytic in D = {z : |z| < 1}.

The main result of this paper (Theorem 1) is that there exist an open set V _E containing X such that every f ∈ B_E can be approximated uniformly on X by functions being analytic in V _E.

Mathematical Subject Classification

Primary: 46.55

Milestones

Received: 30 December 1969

Published: 1 November 1970