Intervals in Generalized Effect Algebras and their Sub-generalized Effect Algebras

Zdenka Riečanová, Michal Zajac

Abstract


We consider subsets G of a generalized effect algebra E with 0∈G and such that every interval [0, q]G = [0, q]E G of G (q G , q ≠ 0) is a sub-effect algebra of the effect algebra [0, q]E. We give a condition on E and G under which every such G is a sub-generalized effect algebra of E.

Keywords


generalized effect algebra; effect algebra; Hilbert space; densely defined linear operators; embedding; positive operators valued state

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague