State spaces of JB*-triples
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, a geometric characterization, up to isometry, of
the unit ball of the dual space of a JB*-triple, extending a theorem of
Friedman and Russo for the atomic case. This result is a non-ordered
analog of the Alfsen-Shultz characterizations of state spaces of
JB-algebras and C*-algebras. As application, by combining this result
with the authors' characterization of TROs ([118] in this archive), an
affine operator space characterization is given of TROs, C*-algebras, and
one-sided ideals in C*-algebras.
(This paper has appeared in Math. Ann. 328 (2004), 585-624)
Matthew Neal < nealm@denison.edu >
Bernard Russo < brusso@math.uci.edu >