We study two subclasses of Banach limits: the one consisting of Banach limits which are invariant with respect of the Cesaro 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.

中文翻译：

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膨胀不变巴拿赫极限

我们研究 Banach 极限的两个子类：一个由对 Cesaro 算子不变的 Banach 极限组成，另一个由对所有膨胀不变的 Banach 极限组成。我们证明第一个是第二个的真子集。我们还表明，这些类与所有 Banach 极限集合的所有极值点的集合 ${\rm ext} \mathfrak B$ 的距离最大。