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Generalized induced norms |
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| Authors: | S Hejazian M Mirzavaziri M S Moslehian |
| Institution: | (1) Department of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad, 91775, Iran |
| Abstract: | Let ‖·‖ be a norm on the algebra ?n of all n × n matrices over ?. An interesting problem in matrix theory is that “Are there two norms ‖·‖1 and ‖·‖2 on ?n such that ‖A‖ = max|‖Ax‖2: ‖x‖1 = 1} for all A ∈ ?n?” We will investigate this problem and its various aspects and will discuss some conditions under which ‖·‖1 = ‖·‖2. |
| Keywords: | induced norm generalized induced norm algebra norm the full matrix algebra unitarily invariant generalized induced congruent |
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