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.

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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

  1. Lorentz G.G. A contribution to the theory of divergent sequences // Acta mathematica. 1948. V. 80. № 1. P. 167–190.
  2. Sucheston L. Banach limits // The American Mathematical Monthly. 1967. V. 74. № 3. P. 308–311.
  3. Mazur S. O metodach sumowalnosci // Ann. Soc. Polon. Math.(Suppl.). 1929. P. 102–107.
  4. Банах С. Теория линейных операций // РХД, М. – Ижевск, 2001. 272 с.
  5. Eberlein W.F. Banach–Hausdorff limits // Proceedings of the American Mathematical Society. 1950. V. 1. № 5. P. 662–665.
  6. Semenov E.M., Sukochev F.A. Invariant Banach limits and applications // Journal of Functional Analysis. 2010. V. 259. № 6. P. 1517–1541.
  7. Semenov E., Sukochev F., Usachev A., Zanin D. Dilation invariant Banach limits // Indagationes Mathematicae. 2020. V. 31. № 5. P. 885–892.
  8. Aliprantis C.D., Burkinshaw O. Positive operators // Academic Press. 1985. 376 p.
  9. 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.
  10. 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.
  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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