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

By B. Solel. 2005

54 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2a7abb8dfea6d404b9d458063b379c968c5d2cd3

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In Algebra and Number Theory

1. Adam H. Fuller
2. E. Kakariadis
3. K. Davidson
4. Orr Shalit

In Geometry and Topology

1. Adam H. Fuller
2. E. Kakariadis
3. K. Davidson

In Mathematical Physics

1. Adam H. Fuller
2. E. Kakariadis
3. K. Davidson
4. Orr Shalit
5. Michael Hartz
6. Martin J. Wainwright

Citations in the corpus

• Semicrossed Products of Operator Algebras by Semigroups (2014, methodology): “This very general construction was introduced by Muhly and Solel [75] based on a construction of Pimsner [87].”
• Subproduct systems (2009, unknown): “Later on Solel, using a different method (using in fact product systems and their representations), proved this result for commuting CP maps on arbitrary von Neumann algebras [41].”