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arXiv · 1911.10748

Matricial Radius: A Relation of Numerical radius with Matricial Range

Mohsen Kian·Mahdi Dehghani·Mostafa Sattari
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Abstract

It has been shown that if $T$ is a complex matrix, then {\small\begin{align*} \omega(T)&=\frac{1}{n}\sup\left\{|\mathrm{Tr}\ X|;\ X\in W^n(T)\right\}\\ &=\frac{1}{n}\sup\left\{\|X\|_1;\ X\in W^n(T)\right\}\\ &= \sup\left\{ \omega(X);\ X\in W^n(T)\right\} \end{align*} } where $n$ is a positive integer, $\omega(T)$ is the numerical radius and $W^n(T)$ is the $n$'th matricial range of $T$.

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Mohsen Kian, Mahdi Dehghani, Mostafa Sattari. 2019-11-25. Matricial Radius: A Relation of Numerical radius with Matricial Range. https://arxiv.org/abs/1911.10748

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