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.
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