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The set of Banach limits and its discrete and continuous subsets
- Authors: Avdeev N.N.1, Zvolinskii R.E.1, Semenov E.M.1, Usachev A.S.1,2
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Affiliations:
- Voronezh State University
- Central South University
- Issue: Vol 518, No 1 (2024)
- Pages: 61-64
- Section: MATHEMATICS
- URL: https://transsyst.ru/2686-9543/article/view/647994
- DOI: https://doi.org/10.31857/S2686954324040092
- EDN: https://elibrary.ru/YYXBPO
- ID: 647994
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Abstract
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.
About the authors
N. N. Avdeev
Voronezh State University
Author for correspondence.
Email: nickkolok@mail.ru
Russian Federation, Voronezh
R. E. Zvolinskii
Voronezh State University
Email: roman.zvolinskiy@gmail.com
Russian Federation, Voronezh
E. M. Semenov
Voronezh State University
Email: nadezhka_ssm@geophys.vsu.ru
Russian Federation, Voronezh
A. S. Usachev
Voronezh State University; Central South University
Email: dr.alex.usachev@gmail.com
Russian Federation, Voronezh; Changsha, Hunan, People's Republic of China
References
- Lorentz G.G. A contribution to the theory of divergent sequences // Acta mathematica. 1948. V. 80. № 1. P. 167–190.
- Sucheston L. Banach limits // The American Mathematical Monthly. 1967. V. 74. № 3. P. 308–311.
- Mazur S. O metodach sumowalnosci // Ann. Soc. Polon. Math.(Suppl.). 1929. P. 102–107.
- 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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