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Izvestiya: Mathematics, 2014, Volume 78, Issue 3, Pages 596–620
DOI: https://doi.org/10.1070/IM2014v078n03ABEH002700 (Mi im8092) 		 
This article is cited in 18 scientific papers (total in 18 papers)

Geometric properties of the set of Banach limits

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

a University of New South Wales
English version PDF (369 kB) Citations (18)
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DOI: https://doi.org/10.1070/IM2014v078n03ABEH002700
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
Received: 16.01.2013
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2014, Volume 78, Issue 3, Pages 177–204
DOI: https://doi.org/10.4213/im8092
Bibliographic databases:
Document Type: Article
UDC: 517.982.22
MSC: 40H05, 46B15, 46B45
Language: English
Original paper language: Russian
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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  • https://doi.org/10.1070/IM2014v078n03ABEH002700
  • https://www.mathnet.ru/eng/im/v78/i3/p177
    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:622
    Russian version PDF:248
    English version PDF:15
    References:67
    First page:40
     
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