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Two equivalent criteria for modularity of the lattice of all physical decision effects

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Abstract

This paper answers the open question 1 of [3] in the affirmative and, conditionally, the open question 2 of [3], too. Assuming irreducibility of the orthomodular latticeG of all physical decision effectsE, we shall prove in the first section that modularity ofG implies symmetry of the physical probability function μ. In the second section, we shall consider the filter algebra ℬ(B′) being assumed to possess an involution * such thatT*T=0 impliesT=0. Then this will be proved: If every atomic filterT P is a fixpoint of * and * is, in a restricted manner, norm-preserving on the minimal left ideal ℒ P :=ℬ(B′)T P , thenG is modular.

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Authors and Affiliations

  1. Mathematisches Institut der Universität Tübingen, Germany

    Günter Dähn

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  1. Günter Dähn
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Dähn, G. Two equivalent criteria for modularity of the lattice of all physical decision effects. Commun.Math. Phys. 30, 69–78 (1973). https://doi.org/10.1007/BF01646689

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  • DOI: https://doi.org/10.1007/BF01646689

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