The geometry of the unit ball of some tensor product spaces

In this work the geometry of the closed unit ball of A⊗MnA⊗Mn is considered, where AA is a uniform algebra acting on a compact Hausdorff space ΩΩ. It is proved that every pure state of A⊗MnA⊗Mn is a Weak∗-exposed point. The closed unit ball of A⊗MnA⊗Mn is also shown to have exposed points if and only if ΩΩ admits a diffuse measure.