On minimal norms on $M_n$

Abstract

In this note, we show that for each minimal norm $N(\cdot )$ on the algebra $M_n$ of all $n\times n$ complex matrices, there exist norms $\Vert \cdot {\Vert }_1$ and $\Vert \cdot {\Vert }_2$ on ${\mathbb{C}}^n$ such that $$N(A)=\max \{\Vert Ax{\Vert }_2:\Vert x{\Vert }_1=1,x\in {\mathbb{C}}^n\}$$ for all $A\in M_n$. This may be regarded as an extension of a known result on characterization of minimal algebra norms.

4 pages, to appear in Abstract and Applied Analysis

References in corpus (1)

• Generalized Induced Norms