An atomic decomposition is proved for Banach spaces which satisfy some affine geometric axioms compatible with notions from the quantum mechanical measuring process. This is then applied to yield, under appropriate assumptions, geometric characterizations, up to isometry, of the unit ball of the dual space of a JB*-triple, and up to complete isometry, of one-sided ideals in C*-algebras.
@article{arxiv.math/0305342,
title = {State spaces of JB*-triples},
author = {Matthew Neal and Bernard Russo},
journal= {arXiv preprint arXiv:math/0305342},
year = {2007}
}