Abstract
We prove that the set of extreme points of the set of dilation–invariant Banach limits is unclosed in the weak\( {}^{*} \) topology.
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Acknowledgments
The author thanks E. M. Semenov and N. N. Avdeev for their perusal of the manuscript and invaluable remarks. The author is also grateful to the referee for the remarks that made it possible to essentially reduce and simplify proofs. In particular, the idea of the proof of Lemma 3 belongs to the referee.
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The author was supported by the Russian Science Foundation (Grant 19–11–00197).
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Usachev, A.S. Extreme Points of the Set of Dilation–Invariant Banach Limits. Sib Math J 61, 895–900 (2020). https://doi.org/10.1134/S0037446620050134
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DOI: https://doi.org/10.1134/S0037446620050134