Nondegenerate Representations of Continuous Product Systems
Operator Algebras
2013-11-20 v3
Abstract
We show that every (continuous) faithful product system admits a (continuous) faithful nondegenerate representation. For Hilbert spaces this is equivalent to Arveson's result that every Arveson system comes from an E_0-semigroup. We point out that for Hilbert modules this is not so. As applications we show a C*-algebra version of a result for von Neumann algebras due to Arveson and Kishimoto, and a result about existence of elementary dilations for (semi-)faithful CP-semigroups.
Cite
@article{arxiv.math/0607362,
title = {Nondegenerate Representations of Continuous Product Systems},
author = {Michael Skeide},
journal= {arXiv preprint arXiv:math/0607362},
year = {2013}
}
Comments
Condensed, to appear in J. Operator Theory