论文标题
$ c $ numerical范围和统一扩张
The $C$-numerical range and Unitary dilations
论文作者
论文摘要
对于$ n \ times n $复杂矩阵$ c $，$ c $ - 数字范围的界限线性运算符$ t $作用在尺寸的希尔伯特（Hilbert）空间上，至少是$ n $的一组$ n $ $ {\ rm tr}（\ rm tr}（cx^*tx）$结果表明，$$ {\ bf cl}（w_c（t））= \ cap \ {{{\ bf cl}（\ bf cl}（w_c（u））：u \ hbox {是} t \} $$的单位扩张，对于任何contraction $ t $，如果$ c $ c $ is Chum c $ is Chum cuns an Chum是一个正常的矩阵，则仅是任何收缩$ t $。
For an $n\times n$ complex matrix $C$, the $C$-numerical range of a bounded linear operator $T$ acting on a Hilbert space of dimension at least $n$ is the set of complex numbers ${\rm tr}(CX^*TX)$, where $X$ is a partial isometry satisfying $X^*X = I_n$. It is shown that $${\bf cl}(W_C(T)) = \cap \{{\bf cl}(W_C(U)): U \hbox{ is a unitary dilation of } T\}$$ for any contraction $T$ if and only if $C$ is a rank one normal matrix.
