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Izv. RAN. Ser. Mat., 2014, Volume 78, Issue 3, Pages 177–204 (Mi izv8092)  

This article is cited in 12 scientific papers (total in 12 papers)

Geometric properties of the set of Banach limits

E. M. Semenov, F. A. Sukocheva, A. S. Usacheva

a University of New South Wales

Abstract: We study the geometry and extreme points of the set $\mathfrak B\subset l_\infty^*$ of all positive normalized shift-invariant functionals on the space $l_\infty$ of all bounded sequences with the uniform norm. In particular, we calculate the radius of $\mathfrak B$ and, for a large class of sequences $x$, describe the orbit of $x$ under the extreme points of $\mathfrak B$.

Keywords: Banach limit, extreme point, almost convergent sequence.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00614-a
Australian Research Council


DOI: https://doi.org/10.4213/im8092

Full text: PDF file (641 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2014, 78:3, 596–620

Bibliographic databases:

UDC: 517.982.22
MSC: 40H05, 46B15, 46B45
Received: 16.01.2013

Citation: E. M. Semenov, F. A. Sukochev, A. S. Usachev, “Geometric properties of the set of Banach limits”, Izv. RAN. Ser. Mat., 78:3 (2014), 177–204; Izv. Math., 78:3 (2014), 596–620

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. A. Alekhno, E. M. Semenov, F. A. Sukochev, A. S. Usachev, “Order properties of the set of Banach limits”, Dokl. Math., 91:1 (2015), 20–22  crossref  crossref  zmath  isi  elib  elib  scopus
    2. I. I. Strukova, “Spektry algebr medlenno menyayuschikhsya i periodicheskikh na beskonechnosti funktsii i banakhovy predely”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2015, no. 3, 161–165  zmath  elib
    3. E. A. Alekhno, “On Banach–Mazur limits”, Indagationes Mathematicae-New Series, 26:4 (2015), 581–614  crossref  mathscinet  zmath  isi  scopus
    4. F. J. Garcia-Pacheco, F. J. Perez-Fernandez, “Fundamental aspects of vector-valued Banach limits”, Izv. Math., 80:2 (2016), 316–328  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. E. A. Alekhno, E. M. Semenov, F. A. Sukochev, A. S. Usachev, “Order and geometric properties of the set of Banach limits”, St. Petersburg Math. J., 28:3 (2017), 299–321  mathnet  crossref  mathscinet  isi  elib
    6. E. Alekhno, E. Semenov, F. Sukochev, A. Usachev, “On the structure of invariant Banach limits”, Comptes Rendus Mathematique, 354:12 (2016), 1195–1199  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. Usachev, F. Sukochev, D. Zanin, “Singular traces and residues of the $\zeta$-function”, Indiana Univ. Math. J., 66:4 (2017), 1107–1144  crossref  mathscinet  zmath  isi
    8. E. Alekhno, E. Semenov, F. Sukochev, A. Usachev, “Invariant Banach limits and their extreme points”, Studia Math., 242:1 (2018), 79–107  crossref  mathscinet  zmath  isi  scopus
    9. E. M. Semenov, F. A. Sukochev, A. Usachev, “The main classes of invariant Banach limits”, Izv. Math., 83:1 (2019), 124–150  mathnet  crossref  crossref  adsnasa  isi  elib
    10. N. N. Avdeev, “On the Space of Almost Convergent Sequences”, Math. Notes, 105:3 (2019), 464–468  mathnet  crossref  crossref  isi  elib
    11. N. N. Avdeev, E. M. Semenov, A. S. Usachev, “Banach Limits and a Measure on the Set of 0-1-Sequences”, Math. Notes, 106:5 (2019), 834–837  mathnet  crossref  crossref  isi
    12. E. M. Semenov, F. A. Sukochev, A. S. Usachev, “Geometriya banakhovykh predelov i ikh prilozheniya”, UMN, 75:4(454) (2020), 153–194  mathnet  crossref
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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