Abstract:Several authors have defined operational quantities derived from the norm of an operator between Banach spaces. This situation is generalized in this paper and we present a general framework in which we derivate several maps $X\rightarrow \Bbb R$ from an initial one $X\rightarrow \Bbb R$, where $X$ is a set endowed with two orders, $\leq $ and $\leq ^{\ast }$, related by certain conditions. We obtain only three different derivated maps, if the initial map is bounded and monotone.
Keywords: derivated map, biordered set, admissible order
AMS Subject Classification: 06A10, 47A53