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Communications in Mathematical Physics

, Volume 30, Issue 1, pp 69–78 | Cite as

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

  • Günter Dähn
Article

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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Probability Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Günter Dähn
    • 1
  1. 1.Mathematisches Institut der Universität TübingenGermany

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