  We theoretically investigate single particle excitations in the BCS
(Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein-Condensation) crossover regime
of an ultracold Fermi gas. Including strong pairing fluctuations within a
$T$-matrix approximation, as well as effects of a harmonic trap potential in
the local density approximation, we calculate the local photoemission spectrum
in the normal state. Recently, JILA group has measured this quantity in a
$^{40}$K Fermi gas, in order to examine homogeneous single-particle properties
of this system. Comparing our results with this experiment, we show that, this
attempt indeed succeeds under the JILA's experimental condition. However, we
also find that the current local photoemission spectroscopy still has room for
improvement, in order to examine the pseudogap phenomenon predicted in the
BCS-BEC crossover region. Since ultracold Fermi gases are always in a trap, our
results would be useful in applying this system to various homogeneous Fermi
systems, as a quantum simulator.
