The set of Banach limits and its discrete and continuous subsets
- 作者: Avdeev N.N.1, Zvolinskii R.E.1, Semenov E.M.1, Usachev A.S.1,2
- 
							隶属关系: 
							- Voronezh State University
- Central South University
 
- 期: 卷 518 (2024)
- 页面: 61-64
- 栏目: MATHEMATICS
- URL: https://rjpbr.com/2686-9543/article/view/647994
- DOI: https://doi.org/10.31857/S2686954324040092
- EDN: https://elibrary.ru/YYXBPO
- ID: 647994
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详细
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.
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	                        作者简介
N. Avdeev
Voronezh State University
							编辑信件的主要联系方式.
							Email: nickkolok@mail.ru
				                					                																			                												                	俄罗斯联邦, 							Voronezh						
R. Zvolinskii
Voronezh State University
														Email: roman.zvolinskiy@gmail.com
				                					                																			                												                	俄罗斯联邦, 							Voronezh						
E. Semenov
Voronezh State University
														Email: nadezhka_ssm@geophys.vsu.ru
				                					                																			                												                	俄罗斯联邦, 							Voronezh						
A. Usachev
Voronezh State University; Central South University
														Email: dr.alex.usachev@gmail.com
				                					                																			                												                	俄罗斯联邦, 							Voronezh; Changsha, Hunan, People's Republic of China						
参考
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- Банах С. Теория линейных операций // РХД, М. – Ижевск, 2001. 272 с.
- Eberlein W.F. Banach–Hausdorff limits // Proceedings of the American Mathematical Society. 1950. V. 1. № 5. P. 662–665.
- Semenov E.M., Sukochev F.A. Invariant Banach limits and applications // Journal of Functional Analysis. 2010. V. 259. № 6. P. 1517–1541.
- Semenov E., Sukochev F., Usachev A., Zanin D. Dilation invariant Banach limits // Indagationes Mathematicae. 2020. V. 31. № 5. P. 885–892.
- Aliprantis C.D., Burkinshaw O. Positive operators // Academic Press. 1985. 376 p.
- Chou C. On the size of the set of left invariant means on a semigroup // Proceedings of the American Mathematical Society. 1969. V. 23. № 1. P. 199–205.
- Семенов Е.М., Сукочев Ф.А., Усачев А.С. Геометрия банаховых пределов и их приложения // Успехи математических наук. 2020. Т. 75. № 4. С. 153–194.
- 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.
- Семенов Е.М., Сукочев Ф.А., Усачев А.С. Структурные свойства множества банаховых пределов // Докл. РАН. 2011. Т. 441. № 2. С. 177–178.
- Semenov E., Sukochev F. Extreme points of the set of Banach limits // Positivity. 2013. Vol. 17. № 1. P. 163–170.
- 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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