Compositions of Sasaki projections |
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Authors: | Georges Chevalier Sylvia Pulmannovà |
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Institution: | (1) Institut de Mathématiques et Informatique, Université Lyon 1, France;(2) Mathematics Institute, Slovak Academy of Sciences, Bratislava, Czechoslovakia |
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Abstract: | In an orthomodular lattice (abbreviated OML) L, a Sasaki projection is a mappinga
x(a)=x(x
va) fromL toL, wherexL. We study compositions of finite numbers of Sasaki projections and of the same Sasaki projections composed in inverse order. By using the Baer-semigroup of all finite compositions of Sasaki projections, we establish a new characterization of kernels of congruences in OMLs and a generalization of the parallelogram law for dimension OMLs. Our results are also related to quantum measurements via Pool's definition of the change of the support of a state after a measurement. |
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Keywords: | |
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