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

On Minimal Norms on Mn

Madjid Mirzavaziri1,2 and Mohammad Sal Moslehian1,3

1Department of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad 91775, Iran
2Banach Mathematical Research Group (BMRG), Mashhad, Iran
3Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University, Iran

Received 18 June 2007; Accepted 19 August 2007

Academic Editor: Allan C. Peterson

Copyright © 2007 Madjid Mirzavaziri and Mohammad Sal Moslehian. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.