Opuscula Math. 41, no. 3 (2021), 437-446
https://doi.org/10.7494/OpMath.2021.41.3.437
Opuscula Mathematica
Quadratic inequalities for functionals in l∞
Gerd Herzog
Peer Chr. Kunstmann
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.
Mathematics Subject Classification: 47B37, 47B48, 47B60.
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- Gerd Herzog (corresponding author)
- Karlsruhe Institute for Technology, Institute for Analysis, D-76128 Karlsruhe, Germany
- Peer Chr. Kunstmann
- Karlsruhe Institute for Technology, Institute for Analysis, D-76128 Karlsruhe, Germany
- Communicated by Alexander Gomilko.
- Received: 2020-11-20.
- Accepted: 2021-01-23.
- Published online: 2021-04-19.
