Inverse continuity on the boundary of the numerical range
Timothy Leake, Brian Lins, Ilya M. Spitkovsky · Linear and Multilinear Algebra · 2013
Let . We consider the mapping , defined on the unit sphere in . The map has a multi-valued inverse , and the continuity properties of are considered in terms of the structure of the set of pre-images for points in the numerical range. It is shown that there may be only finitely many failures of continuity of , and conditions for where these failure occur are given. Additionally, we give a necessary and sufficient condition for weak inverse continuity to hold for and a sufficient condition for .