16 citations · 53 across the 17 of their papers we have counts for
22 papers
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…
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…
Banach synaptic algebras
David J. Foulis, Sylvia Pulmannova
Using a representation theorem of Erik Alfsen, Frederic Schultz, and Erling Stormer for special JB-algebras, we prove that a synaptic algebra is norm complete (i.e., Banach) if and…
A Loomis-Sikorski theorem and functional calculus for a generalized Hermitian algebra
David J. Foulis, Anna Jencova, Sylvia Pulmannova
A generalized Hermitian (GH-) algebra is a generalization of the partially ordered Jordan algebra of all Hermitian operators on a Hilbert space. We introduce the notion of a gh-tri…
Handelman's theorem for an order unit normed space
David J. Foulis, Sylvia Pulmannová
We give a detailed proof D. Handelman's theorem stating (in the context of an order unit normed space) that a monotone sigma-complete order unit normed space is a Banach space.
States and synaptic algebras
David J. Foulis, Anna Jencova, Sylvia Pulmannova
Different versions of the notion of a state have been formulated for various so-called quantum structures. In this paper, we investigate the interplay among states on synaptic alge…