  We investigate the properties of the one-electron Green's function in an
interacting two-dimensional electron system in a strong magnetic field, which
describes an electron tunneling into such a system. From finite-size
diagonalization, we find that its spectral weight is suppressed near zero
energy, reaches a maximum at an energy of about $0.2e^{2}/\epsilon l_{c}$, and
decays exponentially at higher energies. We propose a theoretical model to
account for the low-energy behavior. For the case of Coulomb interactions
between the electrons, at even-denominator filling factors such as $\nu=1/2$,
we predict that the spectral weight varies as $e^{-\omega_0/|\omega|}$, for
$\omega\rightarrow 0$.
