Vector lattices in synaptic algebras

Rok, strany: 2017, 1509 - 1524

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.

ISO 690:

Foulis, D., Jenčová, A., Pulmannová, S. 2017. Vector lattices in synaptic algebras. In Mathematica Slovaca, vol. 67, no.6, pp. 1509-1524. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0066

APA:

Foulis, D., Jenčová, A., Pulmannová, S. (2017). Vector lattices in synaptic algebras. Mathematica Slovaca, 67(6), 1509-1524. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0066