On the unilateral shift as a Hilbert module over the disc algebra
Operator Algebras
2014-05-23 v2 Functional Analysis
Abstract
We study the unilateral shift (of arbitrary countable multiplicity) as a Hilbert module over the disc algebra and the associated extension groups. In relation with the problem of determining whether this module is projective, we consider a special class of extensions, which we call "polynomial". We show that the subgroup of polynomial extensions of a contractive module by the adjoint of the unilateral shift is trivial. The main tool is a function theoretic decomposition of the Sz.-Nagy--Foias model space for completely non-unitary contractions.
Cite
@article{arxiv.1302.6170,
title = {On the unilateral shift as a Hilbert module over the disc algebra},
author = {Raphaël Clouâtre},
journal= {arXiv preprint arXiv:1302.6170},
year = {2014}
}
Comments
21 pages. Final version. Accepted for publication in Complex Analysis and Operator Theory