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Quantum systems and representation theorem

Abstract

In this paper we investigate quantum systems which are locally convex versions of abstract operator systems. Our approach is based on the duality theory for unital quantum cones. We prove the unital bipolar theorem and provide a representation theorem for a quantum system being represented as a quantum \(L^{\infty }\)-system.

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Correspondence to Anar Dosi.

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Dosi, A. Quantum systems and representation theorem. Positivity 17, 841–861 (2013). https://doi.org/10.1007/s11117-012-0208-2

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Keywords

  • Quantum cone
  • Multinormed \(W^{*}\)-algebra
  • Quantum system
  • Quantum order

Mathematics Subject Classification (1991)

  • Primary 46K10
  • Secondary 47L25
  • 47L60