Geodesic
Generating real maps on a biordered set
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 2, pp. 265-272 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 06A06, 06A10, 47A30, 47A53
Keywords: derivated map; biordered set; admissible order 
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Martinon, Antonio. Generating real maps on a biordered set. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 2, pp. 265-272. http://geodesic.mathdoc.fr/item/CMUC_1991_32_2_a7/

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