Numerical range of s(φ)
Numerical range of s(φ)
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s(φ)的数值范围
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
P. Wu
中科院分区：
文献类型：
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作者：
Hwa;P. Wu
研究了有限维Hilbert空间上具有秩(1-T * T)=1性质的完全非酉缩T的数值范围W(T)。我们证明了这类算子完全具有其数值范围的庞塞莱性质，即当且仅当对于单位圆上的任意点λ存在一个(n+l)-gon，该(n+l)-gon内切于单位圆上，以W(T)为界，且以λ为顶点时，n维收缩T属于上述类。我们还得到了这一性质的对偶形式以及任意有限维算子的数值范围内半径的信息。
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+l)-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.