Report
Minkowski product of convex sets and product numerical range
| العنوان: | Minkowski product of convex sets and product numerical range |
|---|---|
| المؤلفون: | Li, Chi-Kwong, Pelejo, Diane Christine, Poon, Yiu-Tung, Wang, Kuo-Zhong |
| سنة النشر: | 2015 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Metric Geometry, 51M15, 15A60 |
| الوصف: | Let $K_1, K_2$ be two compact convex sets in $\mathit{C}$. 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. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1505.05382 |
| رقم الانضمام: | edsarx.1505.05382 |
| قاعدة البيانات: | arXiv |
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1 |
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edsarx arXiv edsarx.1505.05382 952 3 Report report 952.203063964844 |
| PLink |
https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&scope=site&db=edsarx&AN=edsarx.1505.05382&custid=s6537998&authtype=sso |
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