  We investigate pseudogap phenomena originating from pairing fluctuations in
the BCS-BEC crossover regime of a two-dimensional Fermi gas in a harmonic trap.
Including pairing fluctuations within a $T$-matrix theory and effects of a trap
within the local density approximation, we calculate the local density of
states (LDOS) at the superfluid phase transition temperature $T_{\rm c}$. In
the weak-coupling regime, we show that the pseudogap already appears in LDOS
around the trap center. The spatial region where the pseudogap can be seen in
LDOS becomes wider for a strong pairing interaction. We also discuss how the
pseudogap affects the spectrum of the photoemission-type experiment developed
by JILA group.
