On Minimal Norms on $M_n$
Madjid Mirzavaziri and Mohammad Sal Moslehian
Source: Abstr. Appl. Anal. Volume 2007 (2007), 4 pages.
Abstract
We show that for each minimal norm $N(\cdot )$ on the algebra $\mathcal{M}_n$ 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 $A \in \mathcal{M}_n$. This may be regarded as an extension of a known result on characterization of minimal algebra norms.
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Permanent link to this document: http://projecteuclid.org/euclid.aaa/1204126599
Digital Object Identifier: doi:10.1155/2007/52840
Mathematical Reviews number (MathSciNet):
MR2353782
Abstract and Applied Analysis