Unitary extensions of Hilbert A(D)-modules split

Abstract

Let D\subset\mathbb{C}^{n} be a relatively compact strictly pseudoconvex open set or a bounded symmetric and circled domain, and let S denote the Shilov boundary of D. Given Hilbert A(D)-modules H, J and K, we prove that if the A(D)-module structure on H or K extends to a Hilbert C(S)-module structure, then each short exact sequence 0\rightarrow H\rightarrow J\rightarrow K\rightarrow0 splits in the category of Hilbert A(D)-modules.