  The $M_{BH}$ - $\sigma_{\star}$ relation is considered a result of
co-evolution between the host galaxies and their super-massive black holes. For
elliptical-bulge hosting inactive galaxies, this relation is well established,
but there is still a debate whether active galaxies follow the same relation.
In this paper, we estimate black hole masses for a sample of 19 local luminous
AGNs (LLAMA) in order to test their location on the $M_{BH}$ - $\sigma_{\star}$
relation. Super-massive black hole masses ($M_{BH}$) were derived from the
broad-line based relations for H$\alpha$, H$\beta$ and Pa$\beta$ emission line
profiles for the Type 1 AGNs. We compare the bulge stellar velocity dispersion
($\sigma_{\star}$) as determined from the Ca II triplet (CaT) with the
dispersion measured from the near-infrared CO (2-0) absorption features for
each AGN and find them to be consistent with each other. We apply an extinction
correction to the observed broad line fluxes and we correct the stellar
velocity dispersion by an average rotation contribution as determined from
spatially resolved stellar kinematic maps. The H$\alpha$-based black hole
masses of our sample of AGNs were estimated in the range 6.34 $\leq$
$\log{M_{BH}}$ $\leq$ 7.75 M$_\odot$ and the $\sigma_{\star CaT}$ estimates
range between 73 $\leq$ $\sigma_{\star CaT}$ $\leq$ 227 km s$^{-1}$. From the
so-constructed $M_{BH}$ - $\sigma_{\star}$ relation for our Type 1 AGNs, we
estimate the black hole masses for the Type 2 AGNs and the inactive galaxies in
our sample. In conclusion, we find that our sample of local luminous AGNs is
consistent with the $M_{BH}$ - $\sigma_{\star}$ relation of lower luminosity
AGNs and inactive galaxies, after correcting for dust extinction and the
rotational contribution to the stellar velocity dispersion.
