Nondegenerate Representations of Continuous Product Systems

Details Nondegenerate Representations of Continuous Product Systems Nondegenerate Representations of Continuous Product Systems

2006-07-15

arxiv.org/abs/math/0607362v3

Mathematics

Operator Algebras

Condensed, to appear in J. Operator Theory

Scientific paper

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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