Isometric Dilations of Representations of Product Systems via Commutants

Michael Skeide

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arXiv · math/0602459

Isometric Dilations of Representations of Product Systems via Commutants

Michael Skeide

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Abstract

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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Michael Skeide. 2006-02-21. Isometric Dilations of Representations of Product Systems via Commutants. https://arxiv.org/abs/math/0602459

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