Uniformly convex subspaces of measures with the kantorovich norm - Kukharchuk, I.A. (Bulletin of L.N. Gumilyov Eurasian National University. Mathematics, computer science, mechanics series, 2023)
In this paper, we consider signed Borel measures on a compact metric space. We study the uniform convexity of the Kantorovich norm on subspaces of the whole space of signed measures. We construct an example of an infinite-dimensional subspace of measures on which the Kantorovich norm is uniformly convex. We also obtain an example of an infinite compact set (X, ρ) such that all uniformly convex subspaces of the space of measures on X are finite-dimensional.