论文标题
关于道格拉斯代数的同态
On Homomorphisms of Douglas Algebras
论文作者
论文摘要
该论文描述了道格拉斯代数和一些半圣母代数之间的同态。主要工具是连续映射的空间$ c（z，\ mathfrak m）的结构，从连接的首次计算$ t_1 $ t_1 $ space $ z $到达最大理想空间$ \ mathfrak m $ of代数$ h^\ h^\ intemorphic untected holomorphic函数的单位disk $ \ subbb bb d c s subsset $ \ subsset c。特别是，可以表明，从$ z $到$ \ mathbb d $的连续映射空间在$ c（z，\ mathfrak m）$中的点融合拓扑中是密集的，而$ \ mathfrak m $的同型群体是微不足道的。
The paper describes homomorphisms between Douglas algebras and some semisimple Banach algebras. The main tool is a result on the structure of the space $C(Z,\mathfrak M)$ of continuous mappings from a connected first-countable $T_1$ space $Z$ to the maximal ideal space $\mathfrak M$ of the algebra $H^\infty$ of bounded holomorphic functions on the unit disk $\mathbb D\subset\mathbb C$. In particular, it is shown that the space of continuous mappings from $Z$ to $\mathbb D$ is dense in the topology of pointwise convergence in $C(Z,\mathfrak M)$ and the homotopy groups of $\mathfrak M$ are trivial.
