半希尔伯特空间算子的$A$-数值半径正交性与平行性及其应用
$A$-Numerical radius orthogonality and parallelism of semi-Hilbertian space operators and their applications
AI总结：
本文引入并刻画了半希尔伯特空间中算子的$A$-数值半径正交性，证明了$A$-秩一算子的平行性刻画，并应用于算子矩阵的$\mathbb{A}$-数值半径不等式。
摘要：
本文旨在引入并刻画复希尔伯特空间$\mathcal{H}$上关于由正算子$A$诱导的半范数有界的算子的数值半径正交性概念。此外，证明了$A$-秩一算子的$A$-数值半径平行性的一个刻画。作为所得结果的应用，我们得到了算子矩阵的一些$\mathbb{A}$-数值半径不等式，其中$\mathbb{A}$是对角线元素为正算子$A$的算子对角矩阵。还研究了其他一些相关结果。
英文摘要：
In this paper, we aim to introduce and characterize the concept of numerical radius orthogonality of operators on a complex Hilbert space $\mathcal{H}$ which are bounded with respect to the semi-norm induced by a positive operator $A$ on $\mathcal{H}$. Moreover, a characterization of the $A$-numerical radius parallelism for $A$-rank one operators is proved. As applications of the obtained results, we obtain some $\mathbb{A}$-numerical radius inequalities of operator matrices where $\mathbb{A}$ is the operator diagonal matrix with diagonal entries are positive operator $A$. Some other related results are also investigated.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
