Which set is the numerical range of an operator?

Pei Yuan Wu, Hwa Long Gau

研究成果: 雜誌貢獻期刊論文同行評審

1 引文 斯高帕斯(Scopus)

摘要

In this survey paper, we consider the problem of which nonemptybounded convex subset of the complex plane is the numerical range of somebounded linear operator on a complex separable Hilbert space. We startin Section 1 with general operators and move subsequently to operatorsin certain special classes such as normal and hyponormal operators inSection 2, Toeplitz operators in Section 3, Hankel operators in Section 4,compact operators in Section 5, nilpotent operators and roots of identityin Section 6, Sn-matrices and companion matrices in Section 7, and, finally,nonnegative matrices in Section 8. The known main results will be brieflysketched, which are interspersed with relevant unsolved problems.

原文???core.languages.en_GB???
頁(從 - 到)527-545
頁數19
期刊Acta Scientiarum Mathematicarum
88
發行號1-2
DOIs
出版狀態已出版 - 8月 2022

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