MINKOWSKI PRODUCT OF CONVEX SETS AND PRODUCT NUMERICAL RANGE
| dc.citation.epage | 965 | en_US |
| dc.citation.issue | 4 | en_US |
| dc.citation.spage | 945 | en_US |
| dc.citation.volume | 10 | en_US |
| dc.contributor.author | Li, Chi-Kwong | en_US |
| dc.contributor.author | Pelejo, Diane Christine | en_US |
| dc.contributor.author | Poon, Yiu-Tung | en_US |
| dc.contributor.author | Wang, Kuo-Zhong | en_US |
| dc.contributor.department | 應用數學系 | zh_TW |
| dc.contributor.department | Department of Applied Mathematics | en_US |
| dc.date.accessioned | 2017-04-21T06:56:11Z | |
| dc.date.available | 2017-04-21T06:56:11Z | |
| dc.date.issued | 2016-12 | en_US |
| dc.description.abstract | Let K-1, K-2 be two compact convex sets in C. Their Minkowski product is the set K1K2 = {ab : a is an element of K-1, b is an element of K-2}. We show that the set K1K2 is star-haped 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 K1K2 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. | en_US |
| dc.identifier.doi | 10.7153/oam-10-53 | en_US |
| dc.identifier.issn | 1846-3886 | en_US |
| dc.identifier.journal | OPERATORS AND MATRICES | en_US |
| dc.identifier.uri | http://dx.doi.org/10.7153/oam-10-53 | en_US |
| dc.identifier.uri | https://ir.lib.nycu.edu.tw/handle/11536/133273 | |
| dc.identifier.wosnumber | WOS:000393210900008 | en_US |
| dc.language.iso | en_US | en_US |
| dc.subject | Convex sets | en_US |
| dc.subject | Minkowski product | en_US |
| dc.subject | numerical range | en_US |
| dc.title | MINKOWSKI PRODUCT OF CONVEX SETS AND PRODUCT NUMERICAL RANGE | en_US |
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