Unitary extensions of Hilbert A(D)-modules split

Let D ⊂ Cn be a relatively compact strictly pseudoconvex open set or a bounded symmetric and circled domain, and let S denote the Shilov boundary of A(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→H →J →K →0 of Hilbert A(D)-modules splits. In particular, it follows that every Hilbert C(S)-module viewed as an A(D)-module is projective. © 2006 Elsevier Inc. All rights reserved.