Homotonic mappings (Q1910828)

Let \(V\) be a complex linear space of bounded complex-valued functions defined on a set. A functional \(\varphi:V\to\mathbb{C}\) (or a map \(\varphi:V\to V\)) is called homotonic if \(|f|\leq g\) implies \(|\varphi(f)|\leq \varphi(g)\). Examples of homotonic functionals are the spectral radius and the numerical radius of \(n\times n\) complex matrices and some norms for complex matrices. The authors obtain bounds for homotonic functionals in terms of the supremum norm and bounds for homotonic maps in terms of weighted supremum norms.