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Invariant Banach
limits and applications to noncommutative geometry
Evgenii Semenov, Fedor Sukochev, Alexandr Usachev and Dmitriy Zanin |
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Vol. 306 (2020), No. 1, 357–373
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Abstract |
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A linear functional on the space of bounded sequences is called a Banach limit if it is positive, normalised and invariant under the shift operator. There are Banach limits which possess additional invariance properties. We prove that every Banach limit invariant under the Cesaro operator is also invariant under all dilation operators. We also prove the “continuous version” of this result and apply it to the theory of singular traces. |
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Keywords
Banach limit, space of bounded sequences, Cesaro operator,
dilation operator
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Mathematical Subject Classification 2010
Primary: 46B45, 58B34
Secondary: 47B37
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Milestones
Received: 22 March 2018
Revised: 8 June 2019
Accepted: 7 December 2019
Published: 14 June 2020
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Authors |
| Evgenii Semenov | |
| Voronezh State University Voronezh Russia |
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| Fedor Sukochev | |
| School of Mathematics and
Statistics University of New South Wales Sydney Australia |
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| Alexandr Usachev | |
| Department of Mathematical
Sciences Chalmers University of Technology University of Gothenburg Gothenburg Sweden |
School of Mathematics and
Statistics Central South University Hunan China |
| Dmitriy Zanin | |
| School of Mathematics and
Statistics University of New South Wales Sydney Australia |
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