Matricial Radius: A Relation of Numerical radius with Matricial Range

Mohsen Kian, Mahdi Dehghani, Mostafa Sattari

It has been shown that if $T$ is a complex matrix, then {\small\begin{align*} ω(T)&=\frac{1}{n}\sup\left\{|\mathrm{Tr}\ X|;\ X\in W^n(T)\right\}\\ &=\frac{1}{n}\sup\left\{\|X\|_1;\…