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arXiv · 1901.04131

Numerical Range Inclusion, Dilation, and completely positive maps

Chi-Kwong Li·Yiu-Tung Poon
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Abstract

A proof using the theory of completely positive maps is given to the fact that if $A \in M_2$, or $A \in M_3$ has a reducing eigenvalue, then every bounded linear operator $B$ with $W(B) \subseteq W(A)$ has a dilation of the form $I \otimes A$. This gives a unified treatment for the different cases of the result obtained by researchers using different techniques.

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Chi-Kwong Li, Yiu-Tung Poon. 2019-01-14. Numerical Range Inclusion, Dilation, and completely positive maps. https://arxiv.org/abs/1901.04131

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