標題: | Product of operators and numerical range |
作者: | Chien, Mao-Ting Gau, Hwa-Long Li, Chi-Kwong Tsai, Ming-Cheng Wang, Kuo-Zhong 應用數學系 Department of Applied Mathematics |
關鍵字: | numerical range;numerical radius;k-numerical range;k-numerical radius;higher rank numerical range;higher rank numerical radius;47A12;15A60 |
公開日期: | 2-一月-2016 |
摘要: | We show that a bounded linear operator A is an element of B(H) is a multiple of a unitary operator if and only if AZ and Z A always have the same numerical radius or the same numerical range for all (rank one) Z is an element of B(H). More generally, for any bounded linear operators A, B is an element of B(H), we show that AZ and ZB always have the same numerical radius (resp., the same numerical range) for all (rank one) Z is an element of B(H) if and only if A = e(it) B (resp., A = B) is a multiple of a unitary operator for some t is an element of [0, 2 pi). We extend the result to other types of generalized numerical ranges including the k-numerical range and the higher rank numerical range. |
URI: | http://dx.doi.org/10.1080/03081087.2015.1024195 http://hdl.handle.net/11536/129327 |
ISSN: | 0308-1087 |
DOI: | 10.1080/03081087.2015.1024195 |
期刊: | LINEAR & MULTILINEAR ALGEBRA |
Volume: | 64 |
起始頁: | 58 |
結束頁: | 67 |
顯示於類別: | 期刊論文 |