Characterizations of \(^*\)orthant-monotonic norms (Q1318197)

Let \(\mathbb{K}=\mathbb{R}\) or \(\mathbb{C}\). A norm \(p(\cdot)\) on \(\mathbb{K}^ n\) is called \(*\)orthant-monotonic if for every coordinate subspace \(H\subset\mathbb{K}^ n\) the inequality \(p(x)\leq p(x+y)\) \(\forall x\in H\) \(\forall y\in H^ \perp\) holds. The authors give a list of equivalent conditions, characterizing such norms.