Kadison's antilattice theorem for a synaptic algebra

2017/06/06 by David J. Foulis, Foulis, David J., Sylvia Pulmannova +1
Mathematics · #46B40 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:46B40

paper · pdf · doi:10.48550/arxiv.1706.01719

arxiv created 2017/06/06 · arxiv updated 2017/06/07

Abstract

We prove that if A is a synaptic algebra and the orthomodular lattice P of projections in A is complete, then A is a factor iff A is an antilattice. We also generalize several other results of R. Kadison pertaining to infima and suprema in operator algebras.

Related

• Symmetries in Synaptic Algebras
• Two projections in a synaptic algebra
• Orthogonality: An antidote to Kadison's anti-lattice theorem
• Every synaptic algebra has the monotone square root property
• Vector lattices in synaptic algebras