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 ∞ ) \ 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. MSC:30H05, 30H50, 46J15