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

2005/02/20 by Solel, Baruch · 2 citations
#46L08 #46L10 #46L55 #46L57 #47L30 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.math/0502423

Abstract

We study completely contractive representations of product systems of C^*-correspondences over semigroups. For a product system of C^*-correspondences over the semigroup ℕ², 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).

Cited by

• Ando type dilation for completely contractive covariant representations
• An Ando-type dilation on right LCM monoids

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