  We present results of our broadband ellipsometry measurements of the optical
response of ferromagnetic La$_{0.7}$Sr$_{0.3}$CoO$_3$. Our data show that the
ferromagnetic transition is accompanied by a transfer of optical spectral
weight from an absorption band centered at 1.5 eV to a narrow component of the
Drude-like peak. The associated reduction of the intraband kinetic energy is
significantly larger than $k_{\rm B}T_c$, confirming that the double exchange
plays a major role in the ferromagnetism of doped cobaltites. In conjunction
with results of recent theoretical studies, the temperature dependence of the
Drude-like peak suggests that the double exchange is mediated by $t_{2g}$
orbitals.
