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

Baruch Solel

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arXiv · math/0502423

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

Baruch Solel

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Abstract

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).

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BibTeX RIS

Baruch Solel. 2005-12-01. Representations of product systems over semigroups and dilations of commuting CP maps. https://arxiv.org/abs/math/0502423

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