  Let H be a separable Hilbert space with a fixed orthonormal basis (e_n),
n>=1, and B(H) be the full von Neumann algebra of the bounded linear operators
T: H -> H. Identifying l^\infty = C(\beta N) with the diagonal operators, we
consider C(\beta N) as a subalgebra of B(H). For each t in \beta N, let
[\delta_t] be the set of the states of B(H) that extend the Dirac measure
\delta_t. Our main result shows that, for each t in \beta N, this set either
lies in a finite dimensional subspace of B(H)* or else it must contain a
homeomorphic copy of \beta N.
