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.

Extensions and selections in subspaces ofC(K)

“…In the special case when A is a function algebra and q (z) = ~t/2 (z e K) the above follows from [11]; see also [10]. …”