论文标题
$ \ Mathbf {H^\ infty} $地图的密集稳定等级和runge类型定理
Dense Stable Rank and Runge Type Approximation Theorems for $\mathbf{H^\infty}$ Maps
论文作者
论文摘要
令$ h^\ infty（\ mathbb d \ times \ n）$为有界全体形态函数的Banach代数，这些函数在分离式上定义的，可计算的许多副本的开放单位磁盘$ \ MATHBB D \ subset \ subset \ mathbb c $的许多副本。我们表明，$ h^\ infty（\ Mathbb d \ times \ n）$的密集稳定等级是一种，使用此事实证明了一些非线性runge-type近似定理，用于$ h^\ infty（\ mathbb d \ times \ n）$映射。然后，我们将这些结果应用于获得代数$ h^\ infty（\ Mathbb d）$的类似近似问题中近似图的近似图的先验统一估计。
Let $H^\infty(\mathbb D\times\N)$ be the Banach algebra of bounded holomorphic functions defined on the disjoint union of countably many copies of the open unit disk $\mathbb D\subset\mathbb C$. We show that the dense stable rank of $H^\infty(\mathbb D\times\N)$ is one and using this fact prove some nonlinear Runge-type approximation theorems for $H^\infty(\mathbb D\times\N)$ maps. Then we apply these results to obtain a priori uniform estimates of norms of approximating maps in similar approximation problems for algebra $H^\infty(\mathbb D)$.
