Generalized Induced Norms

Details Generalized Induced Norms Generalized Induced Norms

2004-07-21

arxiv.org/abs/math/0407357v1

Czechoslovak Math. J. 57 (2007), no. 1, 127-133

Mathematics

Functional Analysis

8 pages

Scientific paper

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.

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