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[PAST EVENT] Mathematics Colloquium and EXTREEMS-QED Lecture: Chi-Kwong Li (William & Mary)
September 4, 2015
2pm - 3pm
Let $K_1, K_2$ be two compact convex subsets of complex numbers. Their Minkowski product is the set
$K_1K_2 = {ab: a in K_1, b in K_2 }$.
We show that the set $K_1K_2$ is star-shaped if $K_1$ is a line segment or a circular disk. Examples for $K_1$ and $K_2$ are given so that $K_1$ and $K_2$ are triangles (including interior) and $K_1K_2$ is not star-shaped. This gives a negative answer to a conjecture by Puchala et. al concerning the product numerical range in the study of quantum information science.
Additional results and open problems are presented.
$K_1K_2 = {ab: a in K_1, b in K_2 }$.
We show that the set $K_1K_2$ is star-shaped if $K_1$ is a line segment or a circular disk. Examples for $K_1$ and $K_2$ are given so that $K_1$ and $K_2$ are triangles (including interior) and $K_1K_2$ is not star-shaped. This gives a negative answer to a conjecture by Puchala et. al concerning the product numerical range in the study of quantum information science.
Additional results and open problems are presented.
Contact
[[jxshix, Junping Shi]]