Choquet and Shilov Boundaries, Peak Sets, and Peak Points for Real Banach Function Algebras

Abstract

Let be a compact Hausdorff space and let be a topological involution on . In 1988, Kulkarni and Arundhathi studied Choquet and Shilov boundaries for real uniform function algebras on ( , ). Then in 2000, Kulkarni and Limaye studied the concept of boundaries and Choquet sets for uniformly closed real subspaces and subalgebras of ( , ) or ( ). In 1971, Dales obtained some properties of peak sets and p-sets for complex Banach function algebras on . Later in 1990, Arundhathi presented some results on peak sets for real uniform function algebras on ( , ). In this paper, while we present a brief account of the work of others, we extend some of their results, either to real subspaces of ( , ) or to real Banach function algebras on ( , ).