The set of Banach limits and its discrete and continuous subsets

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Resumo

The note states criteria for a Banach limit to belong to discrete or to continuous part of the set of Banach limits. Diameters and radii of these parts are found, too.

Sobre autores

N. Avdeev

Voronezh State University

Autor responsável pela correspondência
Email: nickkolok@mail.ru
Rússia, Voronezh

R. Zvolinskii

Voronezh State University

Email: roman.zvolinskiy@gmail.com
Rússia, Voronezh

E. Semenov

Voronezh State University

Email: nadezhka_ssm@geophys.vsu.ru
Rússia, Voronezh

A. Usachev

Voronezh State University; Central South University

Email: dr.alex.usachev@gmail.com
Rússia, Voronezh; Changsha, Hunan, People's Republic of China

Bibliografia

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  11. Семенов Е.М., Сукочев Ф.А., Усачев А.С. Основные классы инвариантных банаховых пределов // Изв. РАН. Сер. матем. 2019. Т. 83. № 1. С. 140–167.
  12. Семенов Е.М., Сукочев Ф.А., Усачев А.С. Структурные свойства множества банаховых пределов // Докл. РАН. 2011. Т. 441. № 2. С. 177–178.
  13. Semenov E., Sukochev F. Extreme points of the set of Banach limits // Positivity. 2013. Vol. 17. № 1. P. 163–170.
  14. Semenov E., Sukochev F., Usachev A., Zanin D. Invariant Banach limits and applications to noncommutative geometry // Pacific Math. J. 2020. V. 306. № 1. P. 357–373.

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