We report on a study of the temperature and Zeeman-coupling-strength depend
ence of the one-particle Green's function of a two-dimensional (2D) electro
n gas at a Landau-level tilling factor v = 1, where the ground state is a s
trong ferromagnet. Our work places emphasis on the role played by the itine
rancy of the electrons which carry the spin magnetization, and on analogies
between this system and conventional itinerant electron ferromagnets. We g
o beyond self-consistent-held theory by evaluating the one-particle Green's
function using a self-energy, which accounts for quasiparticle spin-wave i
nteractions. Our calculations predict a sharp peak at a large bias voltage
in the 2D-2D tunneling current, with an integrated strength that increases
approximately Linearly with temperature. We compare calculated properties w
ith experiment, where available, and with predictions based on numerical ex
act diagonalization and other theoretical approaches.