  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.
