Mathematics – Functional Analysis
Scientific paper
2007-08-24
Abstr. Appl. Anal. 2007 (2007), Article ID 52840, pp. 4.
Mathematics
Functional Analysis
4 pages, to appear in Abstract and Applied Analysis
Scientific paper
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 $\|\cdot\|_1$ and
$\|\cdot\|_2$ on ${\mathbb C}^n$ such that $$N(A)=\max\{\|Ax\|_2: \|x\|_1=1,
x\in {\mathbb C}^n\}$$ for all $A \in M_n$. This may be regarded as an
extension of a known result on characterization of minimal algebra norms.
Mirzavaziri Madjid
Moslehian Mohammad Sal
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