Monotonicity and \(^*\)orthant-monotonicity of certain maximum norms. (English) Zbl 1038.15017

Let \(\mathbb K\) be the field of real or complex numbers. A characterization of all inner product norms \(p_1\) and \(p_2\) on \(\mathbb K^n\) for which the norm \(x\mapsto \max\{ p_1(x),p_2(x)\}\) on \(\mathbb K^n\) is monotonic or *orthant-monotonic is given.


15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
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