Abstract:In this paper, the $\Cal F$-Riesz norm for ordered $\Cal F$-bimodules is introduced and characterized in terms of order theoretic and geometric concepts. Using this notion, $\Cal F$-Riesz normed bimodules are introduced and characterized as the inductive limits of matricially Riesz normed spaces.
Keywords: Riesz norm, matricially Riesz normed space, positively bounded, absolutely $\Cal F$-convex, $\Cal F$-Riesz norm
AMS Subject Classification: Primary 46L07