2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136233Let 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(βN) with the diagonal operators, we consider C(βN) as a subalgebra of B(H). For each t in βN, let [δ_t] be the set of the states of B(H) that extend the Dirac measure δ_t. Our main result shows that, for each t in βN, this set either lies in a finite dimensional subspace of B(H)* or else it must contain a homeomorphic copy of βN.Operator Algebras46L30, 46L05text