AI 中文总结
本文比较希尔伯特空间算子的几种广义数值半径，建立其关系，证明$(s,t)$-加权数值半径是$t$-加权数值半径的重标形式，为算子相关研究提供工具。
AI 中文摘要
近年来，针对希尔伯特空间上有界线性算子的数值半径，已提出若干推广形式并得到广泛研究，这些推广为研究算子不等式与谱性质提供了更精细的工具。本文研究了几种广义数值半径，建立了它们之间的关系，还发现$(s,t)$-加权数值半径可表示为$t$-加权数值半径的重标形式。
英文摘要
In recent years, several generalizations of the numerical radius for bounded linear operators on Hilbert spaces have been introduced and extensively studied. These generalizations provide refined tools for investigating operator inequalities and spectral properties. In this paper, we investigate several generalized numerical radii and establish relationships among them. We also establish several relationships among these generalized numerical radii and show that the $(s,t)$-weighted numerical radius can be represented as a rescaled form of the $t$-weighted numerical radius.
