There is a long and honorable tradition of using the compact
convex set of states of a C*-algebra as a dual object to shed
light on the algebra. The use of state spaces as a dual object
for C*-algebras was initiated by R. V. Kadison [28,29] who
demonstrated that every C*-algebra can be represented as the
space of continuous affine functions on its state space, and that
every affine homeomorphism between state spaces of C*-algebras
induces a Jordan isomorphism of the algebras. This program was
developed further in the work of Effros [20] and Prosser [37],
who established the connection between closed one-sided ideals of
a C*-algebra and faces of the state space.
In any duality theory, it is important to describe the
possible dual objects) in the context above this amounts to
Received by the editor February 21, 1984
* partially supported by NSF grant # MCS 82-01545
** partially supported by NSF grant # MCS 82 01760
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