Commutants of von Neumann Modules, Representations of B^a(E) and Other Topics Related to Product Systems of Hilbert Modules

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dc.creatorSkeide, Michael
dc.date2003-08-25
dc.date.accessioned2026-07-07T06:30:06Z
dc.date.available2026-07-07T06:30:06Z
dc.descriptionWe review some of our results from the theory of product systems of Hilbert modules. We explain that the product systems obtained from a CP-semigroup in a paper by Bhat and Skeide and in a paper by Muhly and Solel are commutants of each other. Then we use this new commutant technique to construct product systems from E_0-semigroups on B^a(E) where E is a strongly full von Neumann module. (This improves the construction from a paper by Skeide for Hilbert modules where existence of a unit vector is required.) Finally, we point out that the Arveson system of a CP-semigroup constructed by Powers from two spatial E_0-semigroups is the product of the corresponding spatial Arveson systems as defined (for Hilbert modules) in a paper by Skeide. It need not coincide with the tensor product of Arveson systems.
dc.descriptionTo appear in Proceedings of ``Advances in Quantum Dynamics'', Mount Holyoke, 2002
dc.identifierhttps://arxiv.org/abs/math/0308231
dc.identifierhttp://arxiv.org/abs/math/0308231
dc.identifierIn G.L. Price, B.M. Baker, P.E.T. Jorgensen, and P.S. Muhly, editors, Advances in quantum dynamics, number 335 in Contemporary Mathematics, pages 253--262. American Mathematical Society, 2003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98260
dc.subjectOperator Algebras
dc.subjectProbability
dc.subject46L55; 46L53; 60J25; 46L08; 81S25
dc.titleCommutants of von Neumann Modules, Representations of B^a(E) and Other Topics Related to Product Systems of Hilbert Modules
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