Banach synaptic algebras

Abstract

Using a representation theorem of Erik Alfsen, Frederic Schultz, and Erling Stormer for special JB-algebras, we prove that a synaptic algebra is norm complete (i.e., Banach) if and only if it is isomorphic to the self-adjoint part of a Rickart C*-algebra. Also, we give conditions on a Banach synaptic algebra that are equivalent to the condition that it is isomorphic to the self-adjoint part of an AW*-algebra. Moreover, we study some relationships between synaptic algebras and so-called generalized Hermitian algebras.

References in corpus (3)

• Type-Decomposition of a Synaptic Algebra
• States and synaptic algebras
• A Loomis-Sikorski theorem and functional calculus for a generalized Hermitian algebra