  The ability of entangled states to act as resource for teleportation is
linked to a property of the fully entangled fraction. We show that the set of
states with their fully entangled fraction bounded by a threshold value
required for performing teleportation is both convex and compact. This feature
enables for the existence of hermitian witness operators the measurement of
which could distinguish unknown states useful for performing teleportation. We
present an example of such a witness operator illustrating it for different
classes of states.
