On the Ideal Structure of Algebras of Star-Algebra Valued Functions

Abstract

Abstract.The ideal structure of the algebra C(X, A) has been studied in many papers under various topological assumptions on the space X and the algebra A. In this paper we shall study the case where I is a completely regular topological space and A is a locally convex star algebra. In such case the structure of closed (proper) ideals can be described not only by using points of X and some family of closed ideals of A , as usual, but also by using points of the carrier space à.{A) of A and some family of closed ideals of C{X, A) depending on those points and also by using different kind of slice ideals of