Meymand, Ali Ebrahimi \(C^\ast\)-extreme points and \(C^\ast\)-faces of the epigraph if \(C^\ast\)-affine maps in \(\ast\)-rings. (English) Zbl 1438.46081 Wavel. Linear Algebra 5, No. 2, 21-28 (2018). Summary: In this paper, we define the notion of \(C^\ast\)-affine maps in the unital \(\ast\)-rings and we investigate the \(C^\ast\)-extreme points of the graph and epigraph of such maps. We show that for a \(C^\ast\)-convex map \(f\) on a unital \(\ast\)-ring \(\mathcal{R}\) satisfying the positive square root axiom with an additional condition, the graph of \(f\) is a \(C^\ast\)-face of the epigraph of \(f\). Moreover, we prove some results about the \(C^\ast\)-faces of \(C^\ast\)-convex sets in \(\ast\)-rings. Cited in 2 Documents MSC: 46L89 Other “noncommutative” mathematics based on \(C^*\)-algebra theory 52A01 Axiomatic and generalized convexity 16W10 Rings with involution; Lie, Jordan and other nonassociative structures Keywords:\(C^\ast\)-affine map; \(C^\ast\)-convexity; \(C^\ast\)-extreme point; \(C^\ast\)-face PDFBibTeX XMLCite \textit{A. E. Meymand}, Wavel. Linear Algebra 5, No. 2, 21--28 (2019; Zbl 1438.46081)