| Volterra算子及其伴随算子线性组合的数值域 |
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| 引用本文： | 王瑾贤,梁玉霞. Volterra算子及其伴随算子线性组合的数值域[J]. 数学研究及应用, 2023, 43(2): 234-240 |
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| 作者姓名： | 王瑾贤 梁玉霞 |
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| 作者单位： | 天津师范大学数学科学学院, 天津 300387 |
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| 基金项目： | 天津师范大学研究生科研创新项目(Grant No.2022KYCX110Y). |
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| 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$z_1V+z_2V^*(z_1,z_2inmathbb{C})$满足增生性质的等价条件. 本文描述了$(u+iv)I+mV+nV^*(u,v,m,ninmathbb{R},m+ngeq0)$数值域的精确表示.
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| 关 键 词： | Volterra算子 伴随算子 数值域 |
| 收稿时间： | 2022-04-21 |
| 修稿时间： | 2022-06-27 |
Numerical Range of the Linear Combination of Volterra Operator and Its Adjoint |
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| Jinxian WANG,Yuxia LIANG. Numerical Range of the Linear Combination of Volterra Operator and Its Adjoint[J]. Journal of Mathematical Research with Applications, 2023, 43(2): 234-240 |
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| Authors: | Jinxian WANG Yuxia LIANG |
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| Affiliation: | School of Mathematical Science, Tianjin Normal University, Tianjin 300387, P. R. China |
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| Abstract: | 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 $z_1V+z_2V^*(z_1,z_2inmathbb{C})$ satisfies the accretive property. Then an accurate representation of the numerical range of $(u+iv)I+mV+nV^*,(u,v,m,ninmathbb{R},m+ngeq0)$ is described in this paper. |
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| Keywords: | Volterra operator the adjoint operator numerical range |
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