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The Covering Law in Orthomodular Lattices Generated by Graphs of Functions

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Abstract

In the paper [2] we introduced and investigated complete orthomodular lattices generated by graphs of continuous functions. A natural question arises: can such a lattice be represented by the lattice of projectors in a Hilbert space (the standard quantum logic)? The answer is no, because the covering law is not satisfied in this case.

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References

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Authors and Affiliations

  1. Institute of Theoretical Physics, University of Wrocław, pl. Maxa Borna 9, 50–204, Wrocław, Poland

    W. Cegła

  2. Institute of Mathematics, University of Economics, ul. Komandorska 118/120, 53–345, Wrocław, Poland

    J. Florek

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  1. W. Cegła
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  2. J. Florek
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Correspondence to W. Cegła.

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Communicated by M. B. Ruskai

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Cegła, W., Florek, J. The Covering Law in Orthomodular Lattices Generated by Graphs of Functions. Commun. Math. Phys. 268, 853–856 (2006). https://doi.org/10.1007/s00220-006-0116-z

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  • DOI: https://doi.org/10.1007/s00220-006-0116-z

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