Thin sequences in the corona of H∞

Abstract

In this paper we consider several conditions for sequences of points in M(H∞) and establish relations between them. We show that every interpolating sequence for QA of nontrivial points in the corona $$M(H^\infty )\backslash \mathbb{D}$$ of H∞ is a thin sequence for H∞, which satisfies an additional topological condition. The discrete sequences in the Shilov boundary of H∞ necessarily satisfy the same condition.