Definition 13.1.6 (Order Bounded Dual). Let $(E, \le)$ be an ordered vector space, then the space $E^{b}$ consisting of all linear functionals on $E$ that are bounded on order bounded sets is the order bounded dual of $E$.
Definition 13.1.6 (Order Bounded Dual). Let $(E, \le)$ be an ordered vector space, then the space $E^{b}$ consisting of all linear functionals on $E$ that are bounded on order bounded sets is the order bounded dual of $E$.