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On Minimal Norms on Mn

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  • Madjid Mirzavaziri
  • Mohammad Sal Moslehian

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.

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Handle: RePEc:wly:jnlaaa:v:2007:y:2007:i:1:n:052840
DOI: 10.1155/2007/52840
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