On Minimal Norms on Mn

Abstract

We show that for each minimal norm N(⋅) on the algebra ℳn of all n×n complex matrices, there exist norms ‖⋅‖1 and ‖⋅‖2 on ℂn such that N(A)=max{‖Ax‖2:‖x‖1=1, x∈ℂn} for all A∈ℳn. This may be regarded as an extension of a known result on characterization of minimal algebra norms.