C¤-CONVEXITY AND C¤-FACES IN ¤-RINGS

Existence of rich algebraic, geometric and topological structures on self-adjoint operator algebras raises the general question that for a particular theorem which of these structures have made the result working. The present paper is an effort toward the answer of this question, by investigating the role of algebraic structure in the subject of C¤-convexity. In this paper, we extend the notions of C¤-convexity, C¤-extreme point and C¤-face to ¤-rings and we study some of their properties.