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arXiv · 1605.06987

Vector lattices in synaptic algebras

David J. Foulis·Anna Jencova·Sylvia Pulmannova
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Abstract

A synaptic algebra $A$ is a generalization of the self-adjoint part of a von Neumann algebra. We study a linear subspace $V$ of $A$ in regard to the question of when $V$ is a vector lattice. Our main theorem states that if $V$ contains the identity element of $A$ and is closed under the formation of both the absolute value and the carrier of its elements, then $V$ is a vector lattice if and only if the elements of $V$ commute pairwise.

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David J. Foulis, Anna Jencova, Sylvia Pulmannova. 2016-05-23. Vector lattices in synaptic algebras. https://arxiv.org/abs/1605.06987

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