TY  - JOUR
ID  - Herzog2021
LB  - Herzog2021
AU  - Herzog, Gerd
AU  - Kunstmann, Peer Chr.
TI  - Quadratic inequalities for functionals in l<sup>∞</sup>
ST  - Quadratic inequalities for functionals in l<sup>∞</sup>
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2021
VL  - 41
IS  - 3
SP  - 437
EP  - 446
DO  - https://doi.org/10.7494/OpMath.2021.41.3.437
UR  - https://doi.org/10.7494/OpMath.2021.41.3.437
AB  - 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.
KW  - Banach algebras of bounded functions
KW  - operator-invariant functionals
KW  - Banach limits
SN  - 1232-9274
ER  -