  We investigate strong-coupling effects on normal state properties of an
ultracold Fermi gas. Within the framework of $T$-matrix approximation in terms
of pairing fluctuations, we calculate the single-particle density of states
(DOS), as well as the spectral weight, over the entire BCS-BEC crossover region
above the superfluid phase transition temperature $T_{\rm c}$. Starting from
the weak-coupling BCS regime, we show that the so-called pseudogap develops in
DOS above $T_{\rm c}$, which becomes remarkable in the crossover region. The
pseudogap structure continuously changes into a fully gapped one in the
strong-coupling BEC regime, where the gap energy is directly related to the
binding energy of tightly bound molecules. We determine the pseudogap
temperature $T^*$ where the dip structure in DOS vanishes. The value of $T^*$
is shown to be very different from another characteristic temperature $T^{**}$
where a BCS-type double peak structure disappears in the spectral weight. While
one finds $T^*>T^{**}$ in the BCS regime, $T^{**}$ becomes higher than $T^*$ in
the crossover region and BEC regime. Including this, we determine the pseudogap
region in the phase diagram of ultracold Fermi gases. Our results would be
useful in the search for the pseudogap region in ultracold $^6$Li and $^{40}$K
Fermi gases.
