Context : 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 discussion whether active galaxies follow the same relation .

Aims : 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 .
In addition , we test how robustly we can determine the stellar velocity dispersion in the presence of an AGN continuum , AGN emission lines and as a function of signal/noise ratio .

Methods : 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 .

Results : 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 .

Conclusions : 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 .