论文标题
有限对称域的基本正态性的生物形态不变性
The biholomorphic invariance of essential normality on bounded symmetric domains
论文作者
论文摘要
本文主要涉及$ p $ - 在有限的对称域上的$ p $ - 正常性的生物形态不变性。通过建立有关泰勒功能演算的有关合理函数核的新的积分公式，我们证明了与$ p $ - 必不可少的正态性有关的生物形态不变性结果。此外，对于由分析品种确定的商分析性希尔伯特子模型，我们开发了一种代数方法来证明，如果坐标乘数替换为任意的自构式乘数，则保留了$ p $的正态性。此外，压缩元组的泰勒光谱是在温和的条件下计算的，这给出了商subodoules的电晕问题的可溶性结果。作为应用程序，我们将最新结果扩展到$ \ infty $ - 必不可少的正态性和过度汇率之间。
This paper mainly concerns the biholomorphic invariance of $p$-essential normality of Hilbert modules on bounded symmetric domains. By establishing new integral formulas concerning rational function kernels for the Taylor functional calculus, we prove a biholomorphic invariance result related to the $p$-essential normality. Furthermore, for quotient analytic Hilbert submodules determined by analytic varieties, we develop an algebraic approach to proving that the $p$-essential normality is preserved invariant if the coordinate multipliers are replaced by arbitrary automorphism multipliers. Moreover, the Taylor spectrum of the compression tuple is calculated under a mild condition, which gives a solvability result of the corona problem for quotient submodules. As applications, we extend the recent results on the equivalence between $\infty$-essential normality and hyperrigidity.
