Inverse continuity on the boundary of the numerical range

Timothy Leake, Brian Lins, Ilya Spitkovsky

Let $A \in M_n(\C)$. We consider the mapping $f_A(x)=x^{\ast }Ax$, defined on the unit sphere in $\C^n$. The map has a multi-valued inverse $f_A^{-1}$, and the continuity properties of $…