التفاصيل البيبلوغرافية
| 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 |