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- W2950940607 abstract "Let $A in M_n(C)$. We consider the mapping $f_A(x)=x^*Ax$, defined on the unit sphere in $C^n$. The map has a multi-valued inverse $f_A^{-1}$, and the continuity properties of $f_A^{-1}$ 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 $f_A^{-1}$, and conditions for where these failure occur are given. Additionally, we give a necessary and sufficient condition for weak inverse continuity to hold for $n=4$ and a sufficient condition for $n>4$." @default.
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- W2950940607 date "2013-07-18" @default.
- W2950940607 modified "2023-09-27" @default.
- W2950940607 title "Inverse continuity on the boundary of the numerical range" @default.
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