Inspired by Gromov's construction of horofunction compactification, Karlsson [1], [2], among others, started an entire program dedicated to the idea of transposing functional analysis constructions to metric spaces. Central in this realm of ideas is the concept of metric functional. In this work we consider the metric space of metrics, defined on a finite set [3], and obtain the entire description of metric functionals in the first nontrivial cases. [1]Karlsson, A., Elements of a metric spectral theory, Preprint [2]Gouëzel, S., Karlsson, A., Subadditive and multilplicative ergodic theorems To appear in J. Eur. Math. Soc. [3]Khare, A., The non-compact normed space of norms on a finite-dimensional Banach space, arXiv:1810.06188

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Horofunction compactification,Metric space,Metric functional

• Matemáticas - Ciências Naturais