16 citations · 53 across the 17 of their papers we have counts for
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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…
Vector lattices in synaptic algebras
David J. Foulis, Anna Jencova, Sylvia Pulmannova
A synaptic algebra is a generalization of the self-adjoint part of a von Neumann algebra. We study a linear subspace of in regard to the question of when is a vecto…
Lattice pseudo-effect algebras as double residuated structures
David J. Foulis, Sylvia Pulmannova, Elena Vincekova
Pseudo-effect algebras are partial algebraic structures, that were introduced as a non-commutative generalization of effect algebras. In the present paper, lattice ordered pseudo-e…