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math.RA2017
Spectral order on synaptic algebras
David J. Foulis, Sylvia Pulmannova
We define and study an alternative partial order, called the spectral order, on a synaptic algebra-a generalization of the self-adjoint part of a von Neumann algebra. We prove that…
math.RA2017
Kadison's antilattice theorem for a synaptic algebra
David J. Foulis, Sylvia Pulmannova
We prove that if A is a synaptic algebra and the orthomodular lattice P of projections in A is complete, then A is a factor iff A is an antilattice. We also generalize several othe…