Continuously varying peaking functions

John Erik Fornaess and Steven Krantz

Vol. 83 (1979), No. 2, 341–347

DOI: 10.2140/pjm.1979.83.341

Abstract

Let X be a compact metric space, A ⊆ C(X) a closed subalgebra. Let 𝒫⊆ X be the set of peak points for A. It is shown that there is a continuous function Φ : 𝒫→ A such that Φ(x) peaks at x for all x ∈𝒫.

Mathematical Subject Classification 2000

Primary: 54C05

Secondary: 54C99

Milestones

Received: 30 October 1978

Revised: 8 January 1979

Published: 1 August 1979