Spectral and homological properties of Hilbert modules over the disc algebra

Abstract

We study general Hilbert modules over the disc algebra and exhibit necessary spectral conditions for the vanishing of certain associated extension groups. In particular, this sheds some light on the problem of identifying the projective Hilbert modules. Part of our work also addresses the classical derivation problem.

arXiv comment18 pages. Revised version. Accepted for publication in Studia Mathematica