Geometry of Banach limits and their applications

A Banach limit is a positive shift-invariant functional on which extends the functional from the set of convergent sequences to . The history of Banach limits has its origins in classical papers by Banach and Mazur. The set of Banach limits has interesting properties which are useful in applications...

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Bibliographic Details
Published in:Russian mathematical surveys 2020-08, Vol.75 (4), p.725-763
Main Authors: Semenov, E. M., Sukochev, F. A., Usachev, A. S.
Format: Article
Language:English
Subjects:
almost convergent sequences
Banach limits
Cesàro operator
dilation operator
extreme points
invariant Banach limits
non-commutative geometry
singular trace of an operator
Stone-Čech compactification
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Summary:A Banach limit is a positive shift-invariant functional on which extends the functional from the set of convergent sequences to . The history of Banach limits has its origins in classical papers by Banach and Mazur. The set of Banach limits has interesting properties which are useful in applications. This survey describes the current state of the theory of Banach limits and of the areas in analysis where they have found applications. Bibliography: 137 titles.
ISSN:0036-0279
1468-4829
DOI:10.1070/RM9901