  We investigate pseudogap phenomena in the unitarity limit of a trapped
superfluid Fermi gas. Including effect of strong pairing fluctuations within a
$T$-matrix approximation, as well as effects of a harmonic trap within the
local density approximation (LDA), we calculate the local superfluid density of
states below the superfluid phase transition temperature $T_{\rm c}$. We show
that the spatial region where single-particle excitations are dominated by the
pseudogap may still exist even below $T_{\rm c}$, due to inhomogeneous pairing
fluctuations caused by the trap potential. From the temperature dependence of
the pseudogapped density of states, we identify the pseudogap regime of the
unitarity Fermi gas with respect to the temperature and spatial position. We
also show that the combined $T$-matrix theory with the LDA can quantitatively
explain the local pressure which was recently observed in the unitarity limit
of a $^6$Li Fermi gas.
