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Numerical Range Inclusion, Dilation, and completely positive maps (1901.04131v3)
Published 14 Jan 2019 in math.FA
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.