A Dixmier-Schaefer-Zhang theorem for operator algebras

Abstract

Schaefer and Zhang have recently obtained an analogue, for sequentially order continuous functionals on C ( K ) C(K) , of a much earlier theorem of Dixmier. In this note it is shown that the Schaefer-Zhang Theorem has a natural generalisation to non-commutative C ∗ C^* -algebras. These results are obtained as consequences of our main theorem which is concerned with affine functions on compact convex sets.