Abstract and Applied Analysis
Volume 2007 (2007), Article ID 52840, 4 pages
doi:10.1155/2007/52840

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.