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

Document Type: Research Paper


Department of Mathematics, Faculty of mathematical sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.



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(2010): Primary: 52A01; Secondary: 16W10, 46L89.


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