Representations of product systems over semigroups and dilations of commuting CP maps |
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Authors: | Baruch Solel |
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Institution: | Department of Mathematics, Technion, 32000 Haifa, Israel |
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Abstract: | We 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). To achieve this, we first prove that every completely contractive representation of a product system of C∗-correspondences over the semigroup N2 can be dilated to an isometric (or Toeplitz) representation. |
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Keywords: | Completely positive maps Correspondences Product systems Endomorphisms Dilations |
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