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Generalized Induced Norms

Research paper by S. Hejazian, M. Mirzavaziri, M. S. Moslehian

Indexed on: 21 Jul '04Published on: 21 Jul '04Published in: Mathematics - Functional Analysis



Abstract

Let ||.|| be a norm on the algebra M_n of all n-by-n matrices over the complex field C. An interesting problem in matrix theory is that "are there two norms ||.||_1 and ||.||_2 on C^n such that ||A||=max{||Ax||_2: ||x||_1=1} for all A in M_n. We will investigate this problem and its various aspects and will discuss under which conditions ||.||_1=||.||_2.