Unitary extensions of Hilbert A(D)-modules split

摘要

Let D subset of 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 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. (C) 2006 Elsevier Inc. All rights reserved.