论文标题
重新审视福格尔操作员的数值范围
Numerical ranges of Foguel operators revisited
论文作者
论文摘要
Foguel操作员的定义为$ f_t = \ begin {bmatrix} s^*＆t \\ 0＆s \ end end {bmatrix} $，其中$ s $是希尔伯特太空$ \ MATHCAL H $和$ t $的正确移动，可以是$ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ n $。显然，$ w（f_0）$ f_t $的数值范围是$ f_t $，$ t = 0 $是开放单元磁盘，而Gau，Wang和Wu在其LAA'2021论文中建议使用$ W（f_ {ai}）$ for non-Zero $ a \ in \ Mathbb c $ in \ Mathbb c $ in \ Mathbb c $ in \ Mathbb C $可能是一个椭圆形的。在本文中，我们明确地描述了$ w（f_ {ai}）$，但事实并非如此。
The Foguel operator is defined as $F_T=\begin{bmatrix}S^* & T \\ 0 & S\end{bmatrix}$, where $S$ is the right shift on a Hilbert space $\mathcal H$ and $T$ can be an arbitrary bounded linear operator acting on $\mathcal H$. Obviously, the numerical range $W(F_0)$ of $F_T$ with $T=0$ is the open unit disk, and it was suggested by Gau, Wang and Wu in their LAA'2021 paper that $W(F_{aI})$ for non-zero $a\in\mathbb C$ might be an elliptical disk. In this paper, we described $W(F_{aI})$ explicitly and, as it happens, it is not.
