  We have investigated the transport properties of one-dimensional (1D)
constrictions defined by split-gates in high quality GaAs/AlGaAs
heterostructures. In addition to the usual quantized conductance plateaus, the
equilibrium conductance shows a structure close to $0.7(2e^2/h)$, and in
consolidating our previous work [K.~J. Thomas et al., Phys. Rev. Lett. 77, 135
(1996)] this 0.7 structure has been investigated in a wide range of samples as
a function of temperature, carrier density, in-plane magnetic field
$B_{\parallel}$ and source-drain voltage $V_{sd}$. We show that the 0.7
structure is not due to transmission or resonance effects, nor does it arise
from the asymmetry of the heterojunction in the growth direction. All the 1D
subbands show Zeeman splitting at high $B_{\parallel}$, and in the wide channel
limit the $g$-factor is $\mid g \mid \approx 0.4$, close to that of bulk GaAs.
As the channel is progressively narrowed we measure an exchange-enhanced
$g$-factor. The measurements establish that the 0.7 structure is related to
spin, and that electron-electron interactions become important for the last few
conducting 1D subbands.
