Bounded extension property and 𝑝-sets

Abstract

The main result of this paper is a theorem which asserts that a closed subset of the compact Hausdorff space X is a p-set for a uniform algebra A on X if and only if S = { f ∈ A ; Re ⁡ f ⩾ 0 } S = \{ f \in A;\operatorname {Re} f \geqslant 0\} has the so-called bounded extension property with respect to F. Similar results have been obtained by Bishop, Gamelin, Semadeni and the author.