# Some estimates on non-microstates free entropy dimension

Abstract: We give a non-trivial lower estimate for Voiculescu's
non-microstates free entropy dimension. In particular, we show that
for any family of generators of a diffuse von Neumann algebra, the
non-microstates free entropy is at least 1. We also show that for
small values of q, the non-microstates free entropy dimension of
a q-semicircular family of Bozejko and Speicher is strictly larger
than 1.