Nondegenerate Representations of Continuous Product Systems
نویسنده
چکیده
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 E0–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.
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تاریخ انتشار 2009