Maximality in sequences of function algebras

Abstract

AbstractFor a compact subset X of CN (N ∈ N) with non-empty interior a sequence (Bn)n=0∞ of function algebras on X is constructed such that 1.(i) C(X) = B0 ⊃ B1 ⊃ B2 ⊃ …2.(ii) for each n⩾0, Bn+1 is a maximal subalgebra of Bn3.(iii) ∩ Bn={f ∈ C(X): f is analytic on the interior of X}