Wai-Shun Cheung
Published 2016-12-15Version 1
In this article, we are going to search for $n\times n$ matrices $A$ and $B$ such that their generalized numerical range $$W_A(B)=\{tr(AU^*BU) \ :\ U^*U=UU^*=I\}$$ is convex. More specifically, we consider $A=\hat{A}\oplus I_k$ and $B=\hat{B}\oplus I_k$ where $\hat{A}$ and $\hat{B}$ are $2\times 2$. If $W_A(B)=W_{\hat{A}}(\hat{B})$ then it is a convex set.
On Extend the Domain of (Co)convex Polynomial
Denting Points of Convex Sets and Weak Property ($π$) of Cones in Locally Convex Spaces
Sharp Poincaré-type inequality for the Gaussian measure on the boundary of convex sets
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