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Remarks on Effect Algebras

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Abstract

Erik M. Alfsen and Frederic W. Shultz had recently developed the characterisation of state spaces of operator algebras. It established full equivalence (in the mathematical sense) between the Heisenberg and the Schrödinger picture, i.e. given a physical system we are able to construct its state space out of its observables as well as to construct algebra of observables from its state space. As an underlying mathematical structure they used the theory of duality of ordered linear spaces and obtained results are valid for various types of operator algebras (namely C *, von Neumann, JB and JBW algebras). Here, we show that the language they developed also admits a representation of an effect algebra.

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Authors and Affiliations

  1. Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Wita Stwosza 57, 80-952, Gdańsk, Poland

    Władysław A. Majewski

  2. University of Gdańsk, Gdańsk, Poland

    Tomasz I. Tylec

Authors
  1. Władysław A. Majewski
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  2. Tomasz I. Tylec
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Correspondence to Tomasz I. Tylec.

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Majewski, W.A., Tylec, T.I. Remarks on Effect Algebras. Int J Theor Phys 49, 3185–3191 (2010). https://doi.org/10.1007/s10773-009-0226-4

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  • DOI: https://doi.org/10.1007/s10773-009-0226-4

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