Every synaptic algebra has the monotone square root property
Operator Algebras
2016-05-16 v1
Abstract
A synaptic algebra is a common generalization of several ordered algebraic structures based on algebras of self-adjoint operators, including the self-adjoint part of an AW*-algebra. In this paper we prove that a synaptic algebra A has the monotone square property, i.e., if a and b are positive elements, then if a is less or equal than b, then the square root of a is less or equal than the square root of b.
Cite
@article{arxiv.1605.04115,
title = {Every synaptic algebra has the monotone square root property},
author = {David J. Foulis and Anna Jencova and Sylvia Pulmannova},
journal= {arXiv preprint arXiv:1605.04115},
year = {2016}
}