C*-Extreme Points and C*-Faces oF the Epigraph iF C*-Affine Maps in *-Rings

Abstract. In this paper, we define the notion of C*-affine maps in the unital *-rings and we investigate the C*-extreme points of the graph and epigraph of such maps. We show that for a C*-convex map f on a unital *-ring R satisfying the positive square root axiom with an additional condition, the graph of f is a C*-face of the epigraph of f. Moreover, we prove some results about the C*-faces of C*-convex sets in *-rings. Keywords: C*-affine map, C*-convexity, C*-extreme point, C*-face. MSC(۲۰۱۰): Primary: ۵۲A۰۱; Secondary: ۱۶W۱۰, ۴۶L۸۹.

کلیدواژه ها:

C*-affine map ، C*-convexity ، C*-extreme point ، C*-face