Volterra算子及其伴随算子线性组合的数值域

Numerical Range of the Linear Combination of Volterra Operator and Its Adjoint

中文关键词:  Volterra算子  伴随算子  数值域

英文关键词:Volterra operator  the adjoint operator  numerical range

中文摘要:

      经典Volterra算子$V$及其伴随算子$V^*$在复空间$L^2[0,1]$中起着关键作用. 关于$V$和$V^*$的线性组合的性质, 我们给出了确保$z_1V+z_2V^*(z_1,z_2\in\mathbb{C})$满足增生性质的等价条件. 本文描述了$(u+iv)I+mV+nV^*(u,v,m,n\in\mathbb{R},m+n\geq0)$数值域的精确表示.

英文摘要:

      The classical Volterra operator $V$ and its adjoint operator $V^*$ play important roles in the complex space $L^2[0,1]$. As to the properties of linear combination of $V$ and $V^*$, we present the equivalent condition ensuring $z_1V+z_2V^*(z_1,z_2\in\mathbb{C})$ satisfies the accretive property. Then an accurate representation of the numerical range of $(u+iv)I+mV+nV^*\,(u,v,m,n\in\mathbb{R},m+n\geq0)$ is described in this paper.