On Minimal Norms on M_n

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

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Bibliographic Details
Published in:Abstract and Applied Analysis 2007-01, Vol.2007, p.137-140
Main Authors: Mirzavaziri, Madjid, Moslehian, Mohammad Sal
Format: Article
Language:English
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Summary:We show that for each minimal norm N ( ⋅ ) on the algebra ℳ n of all n × n complex matrices, there exist norms ‖ ⋅ ‖ 1 and ‖ ⋅ ‖ 2 on ℂ n such that N ( A ) = max { ‖ A x ‖ 2 : ‖ x ‖ 1 = 1 ,   x ∈ ℂ n } for all A ∈ ℳ n . This may be regarded as an extension of a known result on characterization of minimal algebra norms.
ISSN:1085-3375
1687-0409
DOI:10.1155/2007/52840