  The physical quantity that directly controls the feedback of active galactic
nuclei (AGNs) in elliptical galaxies remains to be determined. The discovery of
molecular gas around the AGNs suggests that the gas is fueling the AGNs.
Therefore, we analyze Atacama Large Millimeter/submillimeter Array (ALMA) data
for the CO line (J=1-0, 2-1, 3-2) emission and estimate the mass of molecular
gas within 500 pc of the center of 12 non-central elliptical galaxies (NCEGs)
and 10 of the brightest cluster galaxies (BCGs). We find that the mass (M_mol ~
10^5-10^9 M_sun) is correlated with the jet power of their AGNs, which is
represented by P_cav ~ 4.1x10^42 (M_mol/10^7 M_sun)^{1.3} erg s^{-1}, although
NCEGs alone do not show the correlation. We also find that M_mol is correlated
with the AGN continuum luminosities at ~ 1.4 GHz (L_1.4) and ~ 100-300 GHz
(L_con). Since P_cav reflects galactic-scale, long-term AGN activity, while the
continuum luminosities reflect local (~< 500 pc), short-term AGN activity, our
results suggest that AGN activity depends on the amount of gas, regardless of
its time scale. On the other hand, we cannot find a clear correlation between
the mass of the black holes in the AGNs (M_BH) and P_cav. This suggests that
M_mol, rather than M_BH, is the main factor controlling AGN activity. We
confirm that the origin of the continuum emission from the AGNs at ~ 1.4-300
GHz is mostly synchrotron radiation.
