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Generalized induced norms

S. Hejazian;  M. Mirzavaziri;  Mohammad Sal Moslehian — 2007

Czechoslovak Mathematical Journal

Let ∥ · ∥ be a norm on the algebra ℳ n of all n × n matrices over ℂ . An interesting problem in matrix theory is that “Are there two norms ∥ · ∥ 1 and ∥ · ∥ 2 on ℂ n such that ∥ A ∥ = max { ∥ A x ∥ 2 ∥ x ∥ 1 = 1 } for all A ∈ ℳ n ?” We will investigate this problem and its various aspects and will discuss some conditions under which ∥ · ∥ 1 = ∥ · ∥ 2 .

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