On Minimal Norms onMn

Abstract

We show that for each minimal normN(⋅)on the algebraℳnof alln×ncomplex matrices, there exist norms‖⋅‖1and‖⋅‖2onℂnsuch thatN(A)=max{‖Ax‖2:‖x‖1=1, x∈ℂn}for allA∈ℳn. This may be regarded as an extension of a known result on characterization of minimal algebra norms.