English

Generalized Induced Norms

Functional Analysis 2021-07-23 v1

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.

Keywords

Cite

@article{arxiv.math/0407357,
  title  = {Generalized Induced Norms},
  author = {S. Hejazian and M. Mirzavaziri and M. S. Moslehian},
  journal= {arXiv preprint arXiv:math/0407357},
  year   = {2021}
}

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8 pages