Uniformly convex subspaces of measures with the kantorovich norm


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Authors

  • I.A. Kukharchuk Moscow State University

DOI:

https://doi.org/10.32523/2616-7182/bulmathenu.2023/2.1

Keywords:

Kantorovich norm, uniformly convex space, subspace of measures, borel signed measures

Abstract

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 $(X, \rho)$ such that all uniformly convex subspaces of the space of measures on $X$ are finite-dimensional.

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Published

2023-06-30

How to Cite

Kukharchuk, I. (2023). Uniformly convex subspaces of measures with the kantorovich norm. BULLETIN OF THE L.N. GUMILYOV EURASIAN NATIONAL UNIVERSITY. Mathematics. Computer Science. Mechanics Series, 143(2), 6–12. https://doi.org/10.32523/2616-7182/bulmathenu.2023/2.1

Issue

Vol. 143 No. 2 (2023)

Section

Статьи