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