Numerical Range Inclusion, Dilation, and completely positive maps

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.

7 pages

Cited by in corpus (1)

• Numerical Range Inclusion, Dilation, and Operator Systems