论文标题
由分析曲线包围的数值范围
Numerical ranges encircled by analytic curves
论文作者
论文摘要
让$ d $在$ \ mathbb {c} $中具有常规分析边界中的一个有限的凸域。假设有界线性运算符$ a $的数值范围$ w（a）$包含在$ \ overline {d} $中。如果$ \ OVILLINE {w（a）} $在无限多点上与边界$ \ partial d $相交，而基本的数值范围$ w_ \ text {ess}（a）$不与$ \ partial d $相交，则$ w（a）= \ edimelline {d} $。这概括了安德森结果的一些无限尺寸类似物。
Let $D$ be a bounded convex domain in $\mathbb{C}$ with a regular analytic boundary. Suppose that the numerical range $W(A)$ of a bounded linear operator $A$ is contained in $\overline{D}$. If $\overline{W(A)}$ intersects the boundary $\partial D$ at infinitely many points while the essential numerical range $W_\text{ess}(A)$ does not intersect $\partial D$, then $W(A) = \overline{D}$. This generalizes some infinite dimensional analogues of a result of Anderson.
