@Article{Herzog2021,
author = "Herzog, Gerd and Kunstmann, Peer Chr.",
title = "Quadratic inequalities for functionals in l<sup>∞</sup>",
journal = "Opuscula Math.",
year = "2021",
volume = "41",
number = "3",
pages = "437--446",
doi = "https://doi.org/10.7494/OpMath.2021.41.3.437",
url = "https://doi.org/10.7494/OpMath.2021.41.3.437",
abstract = "For a class of operators \(T\) on \(l^{\infty}\) and \(T\)-invariant functionals \(\varphi\) we prove inequalities between \(\varphi(x)\), \(\varphi(x^2)\) and the upper density of the sets \[P_r:=\{n \in \mathbb{N}_0: \varphi((T^{n}x)\cdot x) \gt r\}.\] Applications are given to Banach limits and integrals.",
keywords = "Banach algebras of bounded functions, operator-invariant functionals, Banach limits",
issn = "1232-9274"
}