关于Blaschke积连通性的一个注记
A note on connectedness of Blaschke products
摘要：
考虑单位开圆盘上所有内函数的空间$\mathcal{F}$在一致拓扑下的情形，一致拓扑是由$H^{\infty}$ -范数诱导的度量拓扑.本文引入了一类Blaschke积，记为$\mathcal{H}_{SC}$.我们证明了对于每个$B\in\mathcal{H}_{SC}$，$B$和$zB$属于$\mathcal{F}$的同一个路连通分支.它是一种选取优良零点序列的重要方法。作为副产品，我们得到了$\mathcal{H}_{SC}$中的每个Blaschke积都有一个插值的单分量因子.
英文摘要：
Consider the space $\mathcal{F}$ of all inner functions on the unit open disk under the uniform topology, which is a metric topology induced by the $H^{\infty}$-norm. In the present paper, a class of Blaschke products, denoted by $\mathcal{H}_{SC}$, is introduced. We prove that for each $B\in\mathcal{H}_{SC}$, $B$ and $zB$ belong to the same path-connected component of $\mathcal{F}$. It plays an important role of a method to select a fine subsequence of zeros. As a byproduct, we obtain that each Blaschke product in $\mathcal{H}_{SC}$ has an interpolating and one-component factor.
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