%0 Journal Article
%T Representations of product systems over semigroups and dilations of commuting CP maps
%A Baruch Solel
%J Mathematics
%D 2005
%I arXiv
%X 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).
%U http://arxiv.org/abs/math/0502423v2