标题： 多圆盘问题与算子理论和复几何的联系 显示英文标题

标题： Connections of the Corona Problem with Operator Theory and Complex Geometry

摘要： 由H1(D)代数的最大理想空间中开单位圆盘D的稠密性问题，引发了对博里问题的研究。在本文中，我们研究了该问题与算子理论和复几何中的问题之间的关系。 我们使用了希尔伯特模的框架，重点关注复数域Cm中全纯函数的再生核希尔伯特空间。 从这个观点出发，我们解释了对博里问题的几种方法。 在此过程中，做出了一些新的观察。 2012 MSC: 46515, 32A36, 32A70, 30H80, 30H10, 32A65, 32A35, 32A38 关键词：博里问题，希尔伯特模，再生核希尔伯特空间，换位提升定理 显示英文摘要

摘要： The corona problem was motivated by the question of the density of the open unit disk D in the maximal ideal space of the algebra, H1(D), of bounded holomorphic functions on D. In this note we study relationships of the problem with questions in operator theory and complex geometry. We use the framework of Hilbert modules focusing on reproducing kernel Hilbert spaces of holomorphic functions on a domain, in Cm. We interpret several of the approaches to the corona problem from this point of view. A few new observations are made along the way. 2012 MSC: 46515, 32A36, 32A70, 30H80, 30H10, 32A65, 32A35, 32A38 Keywords: corona problem, Hilbert modules, reproducing kernel Hilbert space, commutant lifting theorem 1