Interpolating sequences in a homeomorphic part of $H\sp \infty$

Abstract

Abstract.A characterization of interpolating sequences in a homeomorphic part of the algebra of bounded analytic functions on the unit open disc is given as zero sets of some interpolating Blaschke products.

Interpolating sequences in the maximal ideal space of H∞

“…Then it is not difficult to see that $\{x_{j}\}_{j}$ is not interpolating and $Z(b)\supset\{x_{j}\}_{j}$ . In [3] and [6], they independently proved that if $P$ is a homeomorphic part and $\{x_{j}\}_{j}\subset P$ , then $\{x_{j}\}_{j}$ is interpolating if and only if $\{x_{j}\}_{j}=Z(b)\cap P$ for an interpolating Blaschke product $b$ . In this paper, we study an interpolating sequence whose elements are contained in distinct parts in $G$ .…”

“…The idea to prove our theorem is basically the same as in [6]. The difference between them is; let $h$ be a function in $H^{\infty}$ with $h(x_{1})\neq 0$ and $h(x_{j})=0$ for $j\geqq 2$ and let $B$ be a Blaschke factor of $h$ .…”