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Nondegenerate Representations of Continuous Product Systems

Michael Skeide
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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.

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Michael Skeide. 2009-09-23. Nondegenerate Representations of Continuous Product Systems. https://arxiv.org/abs/math/0607362

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