Isometric Dilations of Representations of Product Systems via Commutants

Details Isometric Dilations of Representations of Product Systems via Commutants Isometric Dilations of Representations of Product Systems via Commutants

2006-02-21

arxiv.org/abs/math/0602459v2

Mathematics

Operator Algebras

Switched some definitions directly after theorems in Sect. 1, included (>6 pp.) introduction to von Neumann correspondences (S

Scientific paper

We construct a weak dilation of a not necessarily unital CP-semigroup to an E-semigroup acting on the adjointable operators of a Hilbert module with a unit vector. We construct the dilation in such a way that the dilating E-semigroup has a pre-assigned product system. Then, making use of the commutant of von Neumann correspondences, we apply the dilation theorem to proof that covariant representations of product systems admit isometric dilations.

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