Uniformly convex subspaces of measures with the kantorovich norm


Views: 152 / PDF downloads: 129

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.

Downloads

Published

2023-06-30

How to Cite

Kukharchuk, I. (2023). Uniformly convex subspaces of measures with the kantorovich norm. Bulletin of 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