On a certain class of operator algebras

algebras. The w*-closure of the pure states of one of these algebras is the set of all states of the algebra. This is not the first example of a C*-algebra whose set of pure states is not closed, cf. [7]. In ?3 we classify the irreducible representations of uniformly hyperfinite algebras according to unitary equivalence. In ??4 and 5 we study certain representations of uniformly hyperfinite algebras.