Representations of product systems over semigroups and dilations of commuting CP maps

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We study completely contractive representations of product systems of $C^*$-correspondences over semigroups. For a product system of $C^*$-correspondences over the semigroup $\mathbb{N}^2$, we prove that every such representation can be dilated to an isometric (or Toeplitz) representation. We use it to prove that every pair of commuting CP maps on a von Neumann algebra $M$ can be dilated to a commuting pair of endomorphisms (on a larger von Neumann algebra).
Revised version. References added. Changes in exposition. To appear in JFA

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Operator Algebras, 46L08, 46L10, 46L55, 46L57, 47L30

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http://salesiana.dossiersoluciones.com/handle/123456789/101087

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0502423
 http://arxiv.org/abs/math/0502423

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arXiv