Product of operators and numerical range

Mao Ting Chien, Hwa Long Gau, Chi Kwong Li, Ming Cheng Tsai, Kuo Zhong Wang

研究成果: 雜誌貢獻期刊論文同行評審

9 引文 斯高帕斯(Scopus)

摘要

We show that a bounded linear operator (Formula presented.) is a multiple of a unitary operator if and only if (Formula presented.) and (Formula presented.) always have the same numerical radius or the same numerical range for all (rank one) (Formula presented.). More generally, for any bounded linear operators (Formula presented.) , we show that (Formula presented.) and (Formula presented.) always have the same numerical radius (resp., the same numerical range) for all (rank one) (Formula presented.) if and only if (Formula presented.) (resp., (Formula presented.)) is a multiple of a unitary operator for some (Formula presented.). We extend the result to other types of generalized numerical ranges including the (Formula presented.) -numerical range and the higher rank numerical range.

原文???core.languages.en_GB???
頁(從 - 到)58-67
頁數10
期刊Linear and Multilinear Algebra
64
發行號1
DOIs
出版狀態已出版 - 2 1月 2016

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