2016/05/13 by David J. Foulis, Foulis, David J., Anna Jencova +3
Mathematics · #47B15 (81P10) #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:47B15
paper · pdf · doi:10.48550/arxiv.1605.04115
arxiv created 2016/05/13 · arxiv updated 2016/05/16
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.