16 citations · 53 across the 17 of their papers we have counts for
5 papers · 1 filter
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.
Synaptic Algebras
D. J. Foulis
A synaptic algebra is both a special Jordan algebra and a spectral order-unit normed space satisfying certain natural conditions suggested by the partially ordered Jordan algebra o…
A projection and an effect in a synaptic algebra
David J. Foulis, Anna Jencova, Sylvia Pulmannova
We study a pair p,e consisting of a projection p (an idempotent) and an effect e (an element between 0 and 1) in a synaptic algebra (a generalization of the self-adjoint part of a…
Two projections in a synaptic algebra
David J. Foulis, Anna Jencova, Sylvia Pulmannova
We investigate P. Halmos' two projections theorem, (or two subspaces theorem) in the context of a synaptic algebra (a generalization of the self-adjoint part of a von Neumann algeb…
Abstract Hermitian Algebras I. Spectral Resolution
David J. Foulis, Sylvia Pulmannova
We refer to the real Jordan Banach algebra of bounded Hermitian operators on a Hilbert space as a Hermitian algebra. We define an abstract Hermitian algebra (AH-algebra) to be the…