Banach synaptic algebras
Rings and Algebras
2018-01-17 v1
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.
Keywords
Cite
@article{arxiv.1705.01011,
title = {Banach synaptic algebras},
author = {David J. Foulis and Sylvia Pulmannova},
journal= {arXiv preprint arXiv:1705.01011},
year = {2018}
}