Abstract:Let $\Bbb K$ be the field of real or complex numbers. In this note we characterize all inner product norms $p_1,\ldots ,p_m$ on $\Bbb K^n$ for which the norm $x \longmapsto \max \{p_1(x),\ldots ,p_m(x)\}$ on $\Bbb K^n$ is monotonic.
Keywords: finite dimensional vector space, monotonic norm, absolute norm, inner product norm
AMS Subject Classification: 52A21