MATHEMATICS

The set of Banach limits and its discrete and continuous subsets

N. N. Avdeev^a, R. E. Zvolinskii^a, E. M. Semenov^a, A. S. Usachev<sup>ab

a</sup> Voronezh State University, Voronezh, Russia
^b Central South University, Changsha

Abstract: Criteria for a Banach limit to belong to the discrete or continuous part of the set of Banach limits are presented. The diameters and radii of these parts are found.

Keywords: Banach limits, invariant Banach limits, diameter and radius of a set.

UDC: 517.982.22

Presented: S. V. Kislyakov
Received: 05.07.2023
Revised: 20.07.2024
Accepted: 24.07.2024

DOI: 10.31857/S2686954324040092

 English version: Doklady Mathematics, 2024, 110:1, 346–348

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