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arXiv · 1910.10899

Dilation invariant Banach limits

Evgenii Semenov·Fedor Sukochev·Alexandr Usachev·Dmitriy Zanin
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Abstract

We study two subclasses of Banach limits: the one consisting of Banach limits which are invariant with respect of the Ces\`aro operator and another one consists of Banach limits which are invariant with respect to all dilations. We prove that the first is a proper subset of the second. We also show that these classes are at the maximal distance from the set ${\rm ext} \mathfrak B$ of all extreme points of the set of all Banach limits.

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Evgenii Semenov, Fedor Sukochev, Alexandr Usachev, Dmitriy Zanin. 2019-10-24. Dilation invariant Banach limits. https://arxiv.org/abs/1910.10899

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