R-CONVEX SUBSETS OF BIMODULES OVER ∗-RINGS

Let M and N be bimodules over the unital ∗-rings R and B, respectively. We investigate the notion of R-convexity and the corresponding notion of R-extreme points. We discuss the effect of an f-homomorphism on R-convex subsets and its R-extreme points. Namely, we declare how an f-homomorphism from M to N carries R-convex subsets and its R-extreme points to B-convex subsets and its B-extreme points and vice versa. Moreover, we confirm that the R-convex hull of invariant subsets under f-homomorphisms remains invariant.