Kadison’s antilattice theorem for a synaptic algebra

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 if and only if A is an antilattice.We also generalize several other results of R. Kadison pertaining to infima and suprema in operator algebras.

Keywords

• synaptic algebra
• order unit space
• Jordan algebra
• spectral resolution
• antilattice
• factor
• Primary 46B40
• Secondary 46L89