RELATIVE BOUNDARIES FOR NORMED SPACES

摘要

We define relative boundaries for subsets of normed spaces. Extending a result of Bishop and de Leeuw, we show that if E is a Banach space and K is a subset of the unit ball of E*, then the (alpha, beta)-points of E relative to K, are strong boundary points of E relative to K. As an application, we show that if A is a unital (left) character amenable Banach algebra, then the spectral Choquet boundary of A is the entire spectrum of A. We give sufficient conditions for character amenability of finitely generated commutative Banach algebras.