摘要
We make a detailed study of the numerical ranges W(T) of completely nonunitary contractions T with the property rank (1-T*T)=1 on a finite-dimensional Hilbert space. We show that such operators are completely characterized by the Poncelet property of their numerical ranges, namely, an n-dimensional contraction T is in the above class if and only if for any point λ on the unit circle there is an (n+1)-gon which is inscribed in the unit circle, circumscribed about W(T) and has λ as a vertex. We also obtain a dual form of this property and the information on the inradii of numerical ranges of arbitrary finite-dimensional operators.
原文 | ???core.languages.en_GB??? |
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頁(從 - 到) | 49-73 |
頁數 | 25 |
期刊 | Linear and Multilinear Algebra |
卷 | 45 |
發行號 | 1 |
DOIs | |
出版狀態 | 已出版 - 1998 |