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Izv. RAN. Ser. Mat., 2019, Volume 83, Issue 1, Pages 140–167 (Mi izv8704)  

The main classes of invariant Banach limits

E. M. Semenova, F. A. Sukochevb, A. Usachevc

a Voronezh State University
b University of New South Wales, School of Mathematics and Statistics, Sidney, Australia
c Department of Mathematical Sciences, Chalmers University of Technology and the University of Göteborg, Göteborg, Sweden

Abstract: We study functional characteristics and extreme points of the set of Banach limits on the space of bounded sequences. We also consider Banach limits with additional invariance properties with respect to the dilation operator and the Cesàro operator.

Keywords: invariant Banach limits, extreme points, Cesàro operator, dilation operator.

Funding Agency Grant Number
Russian Science Foundation 16-11-10125
Austrian Science Fund
The work of the first and third authors is supported by the Russian Science Foundation under grant 16-11-10125. The second author was supported by the Australian Research Council.

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/im8704

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English version:
Izvestiya: Mathematics, 2019, 83:1, 124–150

Bibliographic databases:

UDC: 517.982.22
MSC: 46B15, 46B45
Received: 28.07.2017

Citation: E. M. Semenov, F. A. Sukochev, A. Usachev, “The main classes of invariant Banach limits”, Izv. RAN. Ser. Mat., 83:1 (2019), 140–167; Izv. Math., 83:1 (2019), 124–150

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  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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