Operators defined on the set of Banach limits

S. V. Astashkin^abc, E. M. Semenov^d, A. S. Usachev<sup>e

a</sup> Korolev Samara National Research University, Samara, Russia
^b Lomonosov Moscow State University, Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
^c Bahcesehir University, Istanbul, Turkey
^d Voronezh State University, Voronezh, Russia
^e Central South University, Changsha, China

Abstract: We study invariant subsets of a certain family of nonlinear operators acting on the set of Banach limits. We provide conditions under which an operator from this family coincides with the identity operator. We establish new properties of the extreme points of the set of Banach limits, which indicate their certain mutual independence.

Keywords: Banach limits, extreme points, functional characteristic, invariant subsets.

UDC: 517.982.22

MSC: 35R30

Received: 21.06.2025
Revised: 21.06.2025
Accepted: 10.07.2025

DOI: 10.33048/smzh.2025.66.503

 English version: Siberian Mathematical Journal, 2025, 66:5, 1134–1139