  When a liquid is cooled below its melting temperature it usually
crystallizes. However, if the quenching rate is fast enough, it is possible
that the system remains in a disordered state, progressively losing its
fluidity upon further cooling. When the time needed for the rearrangement of
the local atomic structure reaches approximately 100 seconds, the system
becomes "solid" for any practical purpose, and this defines the glass
transition temperature $T_g$. Approaching this transition from the liquid side,
different systems show qualitatively different temperature dependencies of the
viscosity, and, accordingly, they have been classified introducing the concept
of "fragility". We report experimental observations that relate the microscopic
properties of the {\it glassy phase} to the fragility. We find that the
vibrational properties of the glass {\it well below} $T_g$ are correlated with
the fragility value. Consequently, we extend the fragility concept to the
glassy state and indicate how to determine the fragility uniquely from glass
properties well below $T_g$.
