AI 中文总结
研究可分解的交换等距对，引入核心算子$H(V_1, V_2)$，通过哈托格斯三角形上向量值哈代空间的坐标乘法算子，为满足$H(V_1,V_2)\geq 0$的纯交换等距对建模，并研究核心算子性质及应用。
AI 中文摘要
我们研究可分解为$(V_2V_3,\,V_2)$形式（其中$V_3$为等距算子）的交换等距对$(V_1,V_2)$。为研究此类，引入与交换等距对$(V_1, V_2)$相关的核心算子概念：$H(V_1, V_2):=V_2V_2^*-V_1V_1^*-V_2^2V_2^{*2}+V_1V_2V_1^*V_2^*$。该核心算子与域哈托格斯三角形密切相关。特别地，通过哈托格斯三角形上向量值哈代空间的坐标乘法算子，为满足$H(V_1,V_2)\geq 0$的纯交换等距对建立了一个模型。还研究了核心算子的性质及其在交换等距对中的应用。
英文摘要
We study commuting isometric pairs $(V_1,V_2)$ that admit a factorization of the form $(V_2V_3,\,V_2)$ for some isometry $V_3$. To investigate this class, we introduce the notion of core operator associated with a commuting isometric pair $(V_1, V_2):$ \begin{equation*} H(V_1, V_2):=V_2V_2^*-V_1V_1^*-V_2^2V_2^{*2}+V_1V_2V_1^*V_2^*. \end{equation*} This core operator is closely associated with the domain Hartogs triangle. In particular, we establish a model for pure commuting isometric pairs satisfying $H(V_1,V_2)\geq 0$ via the coordinate multiplication operators on a vector-valued Hardy space over the Hartogs triangle. We also investigate the properties of the core operator and its applications to commuting isometric pairs.
CommentsThis paper presents a new core operator associated with pairs of commuting isometries. I welcome any comments, suggestions, or feedback
